Question

In the given figure, a triangle ABC is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D, are of lengths 4cm and 3cm respectively. If the area of ΔABC =21 cm2 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 the same external point are congruent

Now, we have

AE = AF, BD = BE =4 cm and CD = CF = 3 cm

Now