Statement: The segments of the tangent drawn from a point outside (external point) to a circle are congruent.
Construction: Draw two segments AP and AQ.
According to the figure, A is the centre of the circle. The tangents drawn through point D from outside the circle touches the circle at the points P and Q.
In ∆PAD and ∆QAD,
seg PA ≅ [segQA] [Radii of the same circle]
seg AD ≅ seg AD [Common side]
∠APD = ∠AQD = 90° [Tangent theorem]
∴ ∆PAD = ∆QAD [By Hypotenuse side test]
∴ seg DP = seg DQ [congruent sides of congruent triangles]