+0  
 
+1
810
1
avatar+598 

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?

 Jul 27, 2017
 #1
avatar+21869 
0

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

 

laugh

 Jul 28, 2017

28 Online Users

avatar
avatar