Multiple choice

AB and AC are two chords of a circle. The tangents at B and C meet at P. If ∠BAC = 540, then the measure of ∠BPC is

  1. 360

  2. 540

  3. 720

  4. 1080
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In a circle, the angle between a tangent and a chord through the point of contact equals the angle in the alternate segment. Therefore, ∠PBC = ∠BAC = 54°. Similarly, ∠PCB = ∠BAC = 54°. In triangle BPC, ∠BPC = 180° - (∠PBC + ∠PCB) = 180° - (54° + 54°) = 72°. This is a fundamental property of tangents to circles.

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