[I'm Overwhelmed] Geometry Progress Quiz #10 Q8

GRE Quant Problem Solving
1

Problem: What is the area of an inscribed equilateral triangle in a circle of radius 12?

Round your answer to the nearest integer.

When viewing the solution, Greg mentions that when calculating for the inscribed equilateral triangle height, we know that the ratio of the length from the center to the bottom of the triangle to the radius of the circle (12) is 1:2.

So that means that the length from the center to the bottom of the triangle = 6, therefore the height of the triangle is 18 (12 + 6).

I’m confused as to where this 1:2 ratio came from? I don’t recall it from the videos? Is this only for equilateral triangles?

Thank you for your support in advance!

2

Sketch a figure.

3

I did sketch a figure, but I’m still not understanding how we can conclude the ratio.

4

You’ll find it helpful to divide the triangle into three equilateral parts revolving around the centre of the circle.

Then find the height of any one of the three triangular “parts”.

1 Like
5

Thank you! I finally got it!