Multiple choice

AB and AC are two chords of a circle. The tangents at B and C meet at P. If ∠ BAC=540. Then find the measure of ∠ BPC. AB और AC एक वृत्त के दो जीवायें हैं। B और C पर खीची स्पर्श रेखाएं P पर मिलती हैं। यदि ∠ BAC=540 तो फिर ∠ BPC का माप बताइए।

  1. 1440

  2. 360

  3. 1260

  4. 900
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C Correct answer
Explanation

Using the alternate segment theorem: ∠BPC = 180° - ∠BAC. But ∠BAC = 54° (likely notation error - should be 54° not 540°). So ∠BPC = 180° - 54° = 126°. The angle between the tangents equals the supplement of the angle between the chords. In quadrilateral ABPC, opposite angles sum to 180°.

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