In figure 3.84, O is the centre of the circle. Seg AB, seg AC are tangent segments. Radius of the circle

is r and l(AB) = r, Prove that, ABOC is a square.


Construction: Draw OC and OB.

Given AB and AC are the tangents and r is the radius of the circle.
AB = AC …….(i) [Two tangents from a common point are congruent]
OB = OC = r …(ii) [radii of same circle]
Given AB = r
AB = AC =OB = OC [From (i) and (ii)]
OBA = OCA = 90˚ [Tangent theorem]
ABOC is a square.

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