top button
Flag Notify
    Connect to us
      Site Registration

Site Registration

If each semicircle has a diameter equal to 2, what is the length of AD?

0 votes
251 views

Semicircle AB is flipped upside down and translated horizontally so the new semicircle CD is tangent to AB, as shown. The line through AB is tangent to the semicircle CD and the line through CD is tangent to the semicircle AB.
enter image description here

If each semicircle has a diameter equal to 2, what is the length of AD?
Express your answer in the form √x + √y for positive integers x < y.

posted Oct 4, 2021 by Vikram Luthra

Looking for solution? Promote on:
Facebook Share Button Twitter Share Button LinkedIn Share Button




Similar Puzzles
0 votes
ABCD is a quadrilateral. Point O is along AD. A semicircle has a diameter along AD.............what is the length of AD?

ABCD is a quadrilateral. Point O is along AD. A semicircle has a diameter along AD and is tangent to the sides AB, BC, and CD. If AB = 9, CD = 16, and AO = OD, what is the length of AD?

enter image description here

0 votes
The tangent line to the semicircle has a length of 5 cm. What is the area of the rectangle?

The tangent line to the semicircle has a length of 5 cm. What is the area of the rectangle?
enter image description here

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

A semicircle contains an inscribed semicircle, as shown, dividing its diameter into lengths of 2 and 1. The question has three parts.

I. What is the value y equal to the length of the inscribed semicircle’s diameter?

II. Solve again for the general case if the large diameter is divided into lengths of a and b.

III. Let P be the center of the inscribed semicircle. Solve for the locus of P–that is the set of points P for all possible inscribed semicircles.
enter image description here

enter image description here

enter image description here

0 votes
Rohit has 6 wooden sticks of equal length............At what internal angle he has to join wooden stick with each other?

Rohit has 6 wooden sticks of equal length.
He wants to join all of them in such a way that they make a regular polygon.
At what internal angle he has to join wooden stick with each other?

...