Question

In the circle below, if arc AC = 66 °, and arc BD = 146 °, find the measure of < BPD.

Answer 1

To find the angle BPD we need to remember that the angle formed by two intersecting chords is given by:

$\text{ Angle formed by two intersections=}\frac{1}{2}(\text{ Sum of intercepted arcs\rparen}$

The intercepted arcs are arc AC and arc BD, then we have:

$\begin{gathered} m\angle BPD=\frac{1}{2}(66+146) \\ m\angle BPD=\frac{1}{2}(212) \\ m\angle BPD=106 \end{gathered}$

Therefore, angle BPD is 106° and the answer is option C.