Recent puzzles under tag geometry

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A square with side length 1 is divided into 4 congruent right triangles, as shown, and a square in the center..........

posted Sep 4, 2023 by Kapil Kapoor

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A circle circumscribed 5 squares with side length 1, as shown below. (The squares are in a 2×2 grid and one circle......

posted Aug 30, 2023 by Harshita Dhaliwal

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Let ABC be an equilateral triangle. Let P be any point on its incircle. Prove that: AP2 + BP2 + CP2 = k for some.......

posted Aug 18, 2023 by Saif Khanam

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What is the distance OP you should stand that maximizes the viewing angle APB?

posted Aug 10, 2023 by Pushpak Chauhan

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Three identical squares are shown in the diagram. If the area of the triangle is 1 square meter, what is the area.......

posted Aug 1, 2023 by Anshika Utadi

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Can you think of any three-dimensional shape that comprises exactly two surfaces?

posted Jun 16, 2023 by Pushpak Chauhan

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In the diagram below, 8 identical regular octagons, with side length x, enclose a shape. What is the area.............

posted Jun 14, 2023 by Mridul

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A circle is contained within a rectangle. Tangents to the circle are drawn from each corner of the rectangle............

posted Jun 1, 2023 by Puneet Batra

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Triangle ABC has AB = BC = 10 and AC = 10√2. The triangle is folded so that point A falls on the midpoint M of BC......

posted May 24, 2023 by Aman

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Find the value of m such that R and R‘ have the same area.

posted May 1, 2023 by Vikram Luthra

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A square has side length equal to 1 meter. A circle is constructed through one corner of the square and tangent.........

posted Apr 28, 2023 by Sandeep Otari

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If the large circle has a radius equal to 12, what is a + b + c?

posted Apr 7, 2023 by Karan Joglekar

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A circle has chord PQ. Above the circle (and below it) is a circle tangent to the chord and the large circle...........

posted Mar 14, 2023 by Dilbagh

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A teacher has a rope with length equal to L cm. Using the entire rope, he forms the edges of a non-square rectangle.....

posted Feb 28, 2023 by Nikita Sehgal

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Triangle ABC has a right angle at B. Let Q be along BC and P be along AB........what is the length of the hypotenuse AC?

posted Feb 13, 2023 by Varun Kumar

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Triangle ABC is inscribed in a circle. Construct chord AD and let E be the intersection of chords AD and BC. If AB......

posted Jan 20, 2023 by Sandeep Bedi

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What is the greatest possible area of a triangle with one side of length 7 and another side of length 10?

posted Dec 20, 2022 by Prithvi

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A small circle is contained inside a quarter circle and tangent to one of its sides. A line segment is constructed......

posted Dec 12, 2022 by Nikita Sehgal

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Let ABC be the triangle with AB = 1, AC = 3, and ∠BAC = π/2. If a circle of radius r > 0 touches the sides AB, AC.......

posted Nov 24, 2022 by Nikita Sehgal

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What is the area of AFCE, the region shaded in blue?

posted Nov 9, 2022 by Samardeep Acharya

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Semicircle DE has a right triangle DEF placed over it, where point F is exterior to the semicircle. Let the region......

posted Oct 27, 2022 by Nikhil Pandey

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Solve for the perimeter of a triangle whose altitudes have lengths of 170, 210, and 357.

posted Oct 13, 2022 by Simranjeet Singh

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Dinesh was curious to know the angle between the hour and minute hands of a clock, so when he see10:10 in a clock.......

posted Oct 12, 2022 by Yogeshwar Thakur

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Three spheres are tangent to a plane at the vertices of a triangle and are tangent to each other. Find the radii........

posted Sep 28, 2022 by Sandeep Otari

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A square pyramid has base PQRS and vertex O. Each edge has length equal to 20. Calculate the shortest distance..........

posted Sep 19, 2022 by Prachi Sharma

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A boy started from one corner of a rectangular path and walks along the adjacent sides to reach opposite corner.........

posted Sep 6, 2022 by Karan Joglekar

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A cuboidal block of 8 cm x 12 cm x 20 cm is cut into an exact number of equal cubes. What will be the least possible....

posted Sep 2, 2022 by Yogeshwar Thakur

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In square ABCD, construct M along AB and N along BC. Then construct AN, DM, and CM. Let AN∩DM = P, AN∩CM = Q..........

posted Sep 2, 2022 by Rahul Vaidya

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If PQR is a triangle such that PQ = 15 cm, PR = 15 cm and QR = 18 cm, then what will be the altitude to side PR?

posted Aug 24, 2022 by Upma

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A circle with radius 1 is divided into 12 congruent regions, as shown below. What is the perimeter of a single region?

posted Aug 17, 2022 by Simranjeet Singh

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Square ABCD lies on a flat surface and has regular hexagons attached as flaps on sides AB and AD. Each flap............

posted Aug 11, 2022 by Udita

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What is the distance between the centers of circles X and Y?

posted Jul 12, 2022 by Nikita Sehgal

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Imagine a twelve by twelve square. How many rectangles of any size can you construct from it?

posted Jul 4, 2022 by Varun Kumar

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Three squares are constructed on the three sides of an equilateral triangle. Each......What is the radius of the circle?

posted Jun 22, 2022 by Atif

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In trapezoid ABCD, the sides AB and CD are parallel and AB > CD. Point P is in the interior, dividing the trapezoid.....

posted Jun 3, 2022 by Kapil Kapoor

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Three congruent circles are pairwise tangent and each has a radius equal to 2. A circle circumscribes..............

posted May 18, 2022 by Dilbagh

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A hexagon has interior angles in................What is the measure of largest interior angle of this hexagon?

posted Apr 5, 2022 by Karan Joglekar

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Triangle ABC is an isosceles triangle with AB = AC and A = 100°. Extend the ray........What is the measure of angle BDC?

posted Apr 1, 2022 by Mishthy Mukherjee

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A cuboid with sides in the ratio of 8:5:6 is cut perpendicular...........what is the volume of original cuboid (in cm2)?

posted Mar 23, 2022 by Amarvansh

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In the image below, can you find the value of an angle(y)?

posted Mar 18, 2022 by Nikita Sehgal

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Triangle ABC has sides AB = 8, BC = 7, and AC = 9. The segments AB and AC...............What is the radius of circle O?

posted Mar 4, 2022 by Sidharth Malhotra

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A cyclist starts with a constant speed of 20 km/hr from a corner of a rectangular park and he completes one round.......

posted Feb 23, 2022 by Deepak Chitragar

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A semicircle contains an inscribed semicircle, as shown, dividing its diameter into lengths of 2 and 1.............

posted Feb 11, 2022 by Vikram Luthra

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What is the area of the tilted square?

posted Jan 27, 2022 by Maninder Bath

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Construct a square. Construct 4 semicircles, each with diameter spanning...............what is the area shaded in blue?

posted Dec 31, 2021 by Vikram Luthra

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How many straight lines can be drawn with 26 points on a plane of which no points are collinear?

posted Dec 15, 2021 by Varun Kumar

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Square ABCD is inscribed in a quarter circle O such that B and C are on the arc..........what is the area of the square?

posted Dec 8, 2021 by Karan Joglekar

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You are given a circle with diameter AB and a point C. You are to construct a perpendicular CD to the diameter..........

posted Nov 24, 2021 by Pardeep Kohli

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A circle has two non-intersecting chords AB and CD. Chord RS intersects..................what is the length of chord RS?

posted Nov 18, 2021 by Nikita Sehgal

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What is the length of the common external tangent to two tangent circles of radii 8 inches and 2 inches?

posted Oct 28, 2021 by Rahul Vaidya