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P is a point outside of circle Γ. The tangent from P to Γ touches at A. A line from P intersects Γ at B and C such that m∠ACP = 120∘. If AC=16 and AP=19, find the radius of the circle.

  • Math - ,

    Let O = centre of circle Γ, then
    ∠PAO=90°

  • Math - ,

    Let O = centre of circle Γ, then
    ∠PAO=90°

    Consider ΔPAC,
    use sine rule to find ∠PAC, which
    equals 13° (approx.).

    ∠CAO is therefore 90-∠PAC and equals 77° approx.

    Since Δ CAO is isosceles, with congruent legs equal to the radius r of the circle Γ, and base length = 16, r can be solved.

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