SSC CPO SI and ASI 2016 Paper

Question : 113 of 200

Marks: +1, -0

AB and AC are two chords of a circle. The tangents at B and C meet at P. ∠BAC = 54°, then the measure of ∠BPC is

Solution:

(1)

Since, angle made at center by an arc is double the angle made by the arc at circumference,

∠ B O C=2 ∠ B A C=2 \ ×54^{ ∘}=108^{ ∘}

In quadrilateral PBOC,

\ ∠ B O C+\ ∠ B P C=180^{ °

\ ⇒ ∠ B P C=180-108=72^{ °}

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