Posted by **Leo** on Tuesday, June 4, 2013 at 1:26am.

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 -
**MathMate**, Tuesday, June 4, 2013 at 6:45am
Let O = centre of circle Γ, then

∠PAO=90°

- Math -
**MathMate**, Tuesday, June 4, 2013 at 6:49am
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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