# Department of Science, Math, & Technology

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Circles inside triangles
Posted: Posted June 12th, 2017 by The Fly
 Take any triangle whose sides have length $$a, b, c$$. Find the largest area of a circle that fits inside the triangle. Write down a formula for this area in terms of $$a, b, c$$. Can you find its radius? May the Circles and Triangles be with you. Your best friend, The Fly ============================
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Fly around the circle!

Posted June 12th, 2017 by weid man
weid man

In the case of an isosceles triangle of sides $$a, a, b$$, it only takes an easy calculation to show that the largest embedded circular area is given by

$$\Large{ A = \frac14 \pi b^2 \left(\frac{2a-b}{2a+b}\right) }$$.

Does that seem right to you?

Edited June 18th, 2017 by The Fly
The Fly

In general, could any triangle be mapped to an isosceles triangle by means of a Möbius transformation?

Edited June 18th, 2017 by The Fly
The Fly