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.

Answer 1

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

Answer 2

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.