Question 48
Let $ABC$ be a right triangle with $\angle BAC=90^\circ$, and let $I$ be the intersection of its angle bisectors. A line through $I$ meets sides $AB$ and $AC$ at $P$ and $Q$, respectively. The distance from $I$ to $BC$ is $1~\mathrm{cm}$.
a) Find $PM\cdot NQ$.
b) Find the minimum possible area of triangle $APQ$.
Hint: If $x,y$ are nonnegative real numbers, then $x+y\ge2\sqrt{xy}$.
a) Find $PM\cdot NQ$.
b) Find the minimum possible area of triangle $APQ$.
Hint: If $x,y$ are nonnegative real numbers, then $x+y\ge2\sqrt{xy}$.