Question 38
Triangles $ABC$ and $ABD$ are inscribed in the same semicircle with diameter $AB=15~\mathrm{cm}$. The perpendicular to $AB$ through $D$ meets $AB$ at $P$, segment $AC$ at $Q$, and the extension of $BC$ at $R$. Also, $PR=\frac{40}{3}~\mathrm{cm}$ and $PQ=\frac{15}{4}~\mathrm{cm}$.
a) Verify that $PQ\cdot PR=BP\cdot AP$.
b) Find the length of $DP$.
a) Verify that $PQ\cdot PR=BP\cdot AP$.
b) Find the length of $DP$.