Question

Question 1

Answer 1

1) Because $\angle ACB$ is a central angle, $m\angle ACB=72^{\circ}$.

Since $\angle ACB$ and $\angle BCD$ are supplementary, they form a linear pair, and thus $m\angle BCD=180^{\circ}-72^{\circ}=\boxed{108^{\circ}}$

5) Tangents drawn from an external common point are congruent, so CR=CP=8 and RB=BQ=4. This means that QA=11, and so PA=11 as well. Adding CP+PA, we get AC=19.

6) By the inscribed angle theorem, angle QPR measures 36 degrees.