Multiple choice

If tangents PA and PB from a point P to a circle with centre O are drawn so that ∠APB=80o then ∠POA=? यदि PA और PB स्पर्श रेखा बिन्दु से O केन्द्र वाले वृत्त पर इस प्रकार खींची गयी है कि∠APB=80o तो ∠POA=?

  1. 40o

  2. 50o

  3. 60o

  4. 80o
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B Correct answer
Explanation

PA and PB are equal tangents from external point P to the circle. The radius OA is perpendicular to tangent PA at the point of contact. OP bisects the angle between the two equal tangents, so angle APO = 40 degrees. In right triangle APO, angle POA = 180 - 90 - 40 = 50 degrees.

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