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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