In the given figure, PQ is tangent to the circle with Centre at O, at the point B. If ∠AOB = 100° then ∠ABP, is equal to

Question

Deepak BoraNewbie

Asked: July 30, 20202020-07-30T21:48:31+05:30 2020-07-30T21:48:31+05:30In: CBSE

CBSE 10th Class Mathematics
Past year question paper
Year 2020
SET 1, Code Number – 30/2/1
Question Number – 7
construction geometry [line and circle]
opposite angle

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Deepak Bora · Answer 1 · 2020-07-31T22:11:16+05:30

Deepak Bora Newbie

This answer was edited.

Given that

∠ AOB = 100°

Since OA = OB

So ∠ OAB = ∠ OBA = 40°

Since PQ is tangent on the circle. So OB is perpendicular to PQ.

So,

∠ OBP = 90°

∠ OBA + ∠ ABP = 90°

∠ ABP = 90 – ∠ OBA

∴ ∠ ABP = 90° – 40°

∴ ∠ ABP = 50°