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Ex 10.2 Questions 3

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Ex 10.2 Questions 3

    • Posted by Ayush Kushwah 1 year, 1 month ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Gurjot Kaur 1 year ago

    The radius drawn to the tangents will be perpendicular to the tangents. Thus, OA ⊥ PA and OB ⊥ PB ∠OBP = 90º ∠OAP = 90º In AOBP, Sum of all interior angles = 360° ∠OAP + ∠APB +∠PBO + ∠BOA = 360° 90° + 80° +90º +∠BOA = 360° ∠BOA = 100° In ΔOPB and ΔOPA, AP = BP (Tangents from a point) OA = OB (Radii of the circle) OP = OP (Common side) Therefore, ΔOPB ≅ ΔOPA (SSS congruence criterion) And thus, ∠POB = ∠POA Hence, 50° is the correct answer.

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