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If tangents PA and PB from a point P to a circle with center O are drawn so that ∠APB = 80°, then, ∠POA ?

(a) 40° 

(b) 50°

(c) 80°

(d) 60°

1 Answer

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Best answer

Correct answer is (b) 50°

From △OPA and △OBP

OA = OB   (Radii of the same circle)

 OP (Common side)

PA = PB (Since tangents drawn from an external point to a circle are equal)

\(\therefore \triangle OPA\cong \triangle OPB\) (SSS rule)

\(\therefore \triangle APO=\triangle BPO\)

\(\therefore \angle APO=\frac{1}{2}\angle APB=40^\circ\)

And ∠OAP = 90°

(Since tangents drawn from an external point are perpendicular to the radius at point of contact)

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