Prove that the tangents drawn at the ends of a chord of a circle make equal angles with the chord.

Given: l and m are tangents intersecting at A and touching the circle at B and C.
To prove:
(i) ∠ ABC = ∠ ACB              

(ii) ∠ XBO = ∠ OCY

Proof:
(i) Using the theorem, the length of the tangents drawn form an external point to a circle are equal.
∠ ABC = ∠ ACB (∵ Sides opposite to equal angles are equal)
(ii) Using the theorem, the tangent at any point of a circle is perpendicular to the radius through the point of contact.
∠ XBO = 90°
∠ OCY = 90°
∠ XBO = ∠ OCY.