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Let $\triangle ABC$ be an isosceles triangle such that $BC = 30$ and $AB = AC.$ We have that $I$ is the incenter of $\triangle ABC,$ and $IC = 18.$ What is the length of the inradius of the triangle?

michaelcai  Jul 27, 2017
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Let triangle ABC be an isosceles triangle such that BC = 30 and AB = AC.
We have that I is the incenter of triangle ABC, and IC = 18.
What is the length of the inradius of the triangle?

$$\begin{array}{|rcll|} \hline \left( \frac{30}{2} \right)^2 + r^2 &=& 18^2 \\ 15^2 + r^2 &=& 18^2 \\ r^2 &=& 18^2-15^2 \\ r^2 &=& 324-225 \\ r^2 &=& 99 \\ r^2 &=& 9\cdot 11 \\ r &=& 3\cdot \sqrt{11} \\ \hline \end{array}$$

r = 9.95

heureka  Jul 28, 2017