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Question
In the given figure, PA is a tangent to the circle drawn from the external point P and PBC is the secant to the circle with BC as diameter. If ∠AOC = 130°, then find the measure of ∠APB, where O is the centre of the circle.
Solution
In ΔAPO, ∠AOC is the exterior angle
∴ From exterior angle property.
∠AOC = ∠PAO + ∠APB ...`{{:(∵ ∠AOC = 130^circ ("Given")),(∠PAO = 90^circ "(radius and tangent"),("are" ⊥ "to each other at the point of contact)"):}`
`\implies` 130° = 90° + ∠APB
`\implies` ∠APB = 130° – 90°
`\implies` ∠APB = 40°
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