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Question

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


(a) 40°
(b) 50°
(c) 80°
(d) 60°

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Solution

(b) 50°

From OPA and OPB,OA=OB Radii of the same circleOP (Common side)PA=PB Since tangents drawn from an external point to a circle are equalOPA OPB SSS ruleAPO=BPOAPO=12APB=400 And OAP=900 (Since tangents drawn from an external point areperpendicular to the radius at point of contact)Now, inOAP, AOP+OAP+APO=1800AOP+900+400=1800AOP=1800-1300=500




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