Question

In the given figure, a triangle ABC is drawn to circumscribe a circle of radius 3 cm such that the segments BC and DC into which BC is divided by the point of contact D, are of lengths 6cm and 9cm respectively. if the area of ΔABC = 54cm² then find the lengths of sides AB and AC.

Answer 1

Construction: Join OA, OB, OC, OE ⊥ AB at E and OF ⊥ AC at f

We know that tangent segments to a circle from me same external point are congruent Now, we have

AE = AF, BD = BE = 6 cm and CD = CF

Now,