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=}(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=(1)/(2)(66+146) \\ m\angle BPD=(1)/(2)(212) \\ m\angle BPD=106 \end{gathered}`

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