In a large equilateral triangle, we draw the incircle. In the incircle, we draw another equilateral triangle...

In a large equilateral triangle, we draw the incircle. In the incircle, we draw another equilateral triangle.
What is the ratio of the area of the smaller equilateral triangle to the larger equilateral triangle?

1 Answer

Answer is 1:4
the ratio of the area of the smaller equilateral triangle to the larger equilateral triangle is 1:4

answer Sep 13, 2017 by Mogadala Ramana

Similar Puzzles

0 votes

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

Let ABC be an equilateral triangle. Let P be any point on its incircle. Prove that:

AP2 + BP2 + CP2 = k
for some constant k

0 votes

A polygon has exactly one side which length is 2 other sides are 1. Is it possible to draw an incircle to polygon?

A polygon has exactly one side which length is 2, other sides' length are 1. Is it possible to draw an incircle to polygon?

Note: An incircle touches every side of a polygon and completely drawn within the polygon?

0 votes

Let ABC be a triangle with AB < AC < BC. Let the incentre and incircle of triangle ABC be I and ω, respectively.........

Let ABC be a triangle with AB < AC < BC. Let the incentre and incircle of triangle ABC be I and ω, respectively. Let X be the point on the line BC different from C such that the line through X parallel to AC is tangent to ω. Similarly, let Y be the point on the line BC different from B such that the line through Y parallel to AB is tangent to ω. Let AI intersect the circumcircle of triangle ABC again at P ≠ A. Let K and L be the midpoints of AC and AB, respectively.
Prove that ∠KIL + ∠YPX = 180°.