Triangles in Circles

Geometry Level 2

Rutwik was doodling around in math class and drew the two circles as shown in the diagram.

After giving it a thought Rutwik came up with a hypothesis and calls it R u t w i k ′ s H y p o t h e s i s Rutwik's \ Hypothesis .

Here's his hypothesis.

Rutwik's Hypothesis : The G R E E N GREEN triangle and the B L U E BLUE triangle are similar if and only if the segment a a is parallel to segment b b .

What do you think about his hypothesis ?

Rutwik is smart...(His hypothesis is correct) Rutwik needs to pay attention in math class...(His hypothesis is incorrect)

A Former Brilliant Member by A Former Brilliant Member

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2 solutions

Here is a counterfeiting example.

The triangles can also be similar if the two segments are congruent (As shown in the diagram).

The statement is false because of the "if and only if part".

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Marta Reece
Jul 9, 2017

The two triangles are similar if the two segments are not parallel and not equal to each other as well.

All angles of both triangles are the same. Angles at A and B are the same as they are both over the arc CD.

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