Deepak Bora
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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

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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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1 Answer

  1. 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°

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