Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.

Lets assume a circle with radius =r and AP and AQ are two external tangents and ∠PAQ=60° be the angle between them. Therefore ∠CAP=θ and ∠CPA=90°. So in ΔCAP, sinθ=sin(60°/2)=CP/CA. sin(30°)=5/CA. CA=10cm. Now lets construct this pair of tangents. Construct a circle with centre c and radius=5cm. Locate a point A, which is 10cm for C such that CA=10cm. Now locate the midpoint of CA be M so that CM=MA=5cm. Now draw a circle with centre M and radius=CM=5cm and assume that this circle intersects the previous circle at points P and Q and join the points P,A and Q,A. So that PA and QA are our desire tangents such that ∠PAQ=60°