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From a point p, two tangents …

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From a point p, two tangents PA and PB are drawn to a circle with centre o. If OP = diameter of the circle , show that ∆APB is equilateral.

Posted by Shraddha Sharma 7 years, 9 months ago

CBSE > Class 10 > Mathematics

1 answers

Chandrashekhar Wankhede 7 years, 9 months ago

Triangle OAP will be right angles triangle, OA = r, OP = 2r, angle OAP = 90 as tangent is perpendicular to radius, sin ( APO) = r / (2r) = 1/2, hence angle APO = 30. similarly angle BPO = 30, hence angle APB = 60 . But AP = BP as tangent segments from external point are equal, hence triangle APB is ISO triangle with one angle 60 , hence other two angles are also 60

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