# #21 of Sept 2017 Grade 10 CSAT (Korean SAT) Mock test

Geometry Level 3

Triangle $$ABC$$ has side lengths $$\overline{AB}=2\sqrt{3}$$ and $$\overline{BC}=2,$$ as shown. $$D$$ is the midpoint of $$\overline{BC},$$ satisfying $$\overline{AD}=\sqrt{7}.$$

Let $$E$$ be the point of intersection between $$\overline{AB}$$ and the bisector of $$\angle ACB.$$ $$\overline{CE}$$ meets with $$\overline{AD}$$ at point $$P,$$ and the bisector of $$\angle APE$$ meets with $$\overline{AB}$$ at point $$R.$$ An extension of $$\overline{PR}$$ meets with $$\overline{BC}$$ at point $$Q.$$

Given that the area of $$\triangle PQC$$ is $$a+b\sqrt{7}$$ times larger than that of $$\triangle PRE$$ for some rational numbers $$a$$ and $$b,$$ find the value of $$ab.$$

This problem is a part of <Grade 10 CSAT Mock Test> series.

×

Problem Loading...

Note Loading...

Set Loading...