Question

In Fig. 10.68, a is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC are of lengths 8 cm and 6 cm respectively. Find the lengths of sides AB and AC, when area of is 84 cm².

Answer 1

The lengths of sides AB and AC, when area of triangle is 84 cm-

Extend the line OD till it meets A. Therefore, AD becomes height of - ΔABC with ∠ADC = 90° and BC forms the base (tangent to the circle).

Length of BC = 14cm

Length of AD = 4 + x (Assuming OA as x)

-Area of ΔABC = 1/2 × base × height

1/2 × 14 × (4+x) = 84cm²

4 + x = 12 ; x = 8cm

therefore, height of ΔABC = 4+8 = 12cm

Applying pythagoras theorem in ΔADC, AD² + DC² = AC²

12² + 6² = AC² ; 144 + 36 = AC²

AC² = 180 ; AC = 6√5

Similarly, in ΔADB, AD² + DB² = AB²

12² + 8² = AB² ; 144 + 64 = AB²

AB² = 208 ; AB = 4√13