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in triangle apb....
angle apb =60°
side ap =side pb (two tangent meets at a point outside the circle are equal)
so, angle pab = angle abp ( angle opp. to equal sides are equal)
so in this angle A +B+P=180°
that is 60°+A+A=180°[A=B]
60°+2A=180°
2A=120°
A=60°
so,
oa is perpendicular to tangent pa(radius is perpendicular to tangent)
angle oap =90°
now angle oab = angle oap- angle bap
angle oab= 90°-60°=30°
so angle oab = 30°
angle apb =60°
side ap =side pb (two tangent meets at a point outside the circle are equal)
so, angle pab = angle abp ( angle opp. to equal sides are equal)
so in this angle A +B+P=180°
that is 60°+A+A=180°[A=B]
60°+2A=180°
2A=120°
A=60°
so,
oa is perpendicular to tangent pa(radius is perpendicular to tangent)
angle oap =90°
now angle oab = angle oap- angle bap
angle oab= 90°-60°=30°
so angle oab = 30°
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