Question

DUDA
A triangle ABC is drawn to circumscribe a circle of radius 3 cm.
such that the segments BD and DC into which BC is divided by
the point of contact D are of length 9 cm. and 3 cm. respectively
(See adjacent figure). Find the sides AB and AC.
cm.​

Answer 1

FIRST OF ALL THIS TRIANGLE SHOULD BE RIGHT ANGLED

SINCE TRIANGLE ABC CIRCUMSCRIBE THE CIRCLE

BD IS A TANGENT AND LET US ASSUME BA INTERSECT AT E THEN BE=9cm LET AE be X

THEN

BY PGT

AB²=BC²+AC²

(9+X)²=(12)²+(X)²

81+X²+18X=144+X²

18X=144-81

X=63/18 = 21/6=7/2 =3.5cm

NOW AB = 9+3.5=12.5CM

and AC = 6.5CM