Q12 of 31 Page 218

In the adjoining figure, ΔABC circumscribed a circle and touches the points P,Q,R. If AP = 4 cm, BP = 6cm, AC = 12 cm and BC = x cm, let us determine the value of x.

AP = 4 cm


BP = 6cm


AC = 12 cm


AP = AR = 4 cm (Tangents drawn from an external point to the same circle are always equal)


CR = (AC-AR) = 8 cm


CR = CQ = 8 cm (Tangents drawn from an external point to the same circle are always equal)


BP = BQ = 6 cm (Tangents drawn from an external point to the same circle are always equal)


x = BC = (BQ + CQ) = 14 cm


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In the adjoining figure, two tangents drawn from external point C to a circle with centre O touches the circle at the points P and Q respectively. A tangent drawn at another point R of a circle intersects CP and CA at the points A and B respectively. If CP = 11 cm. and BC = 7cm, let us determine the length of BR.