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

In the circle below, if arc AC = 66 °, and arc BD = 146 °, find the measure of &lt-example-1

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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.

User Remul
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