Question

The radii of two concentric circles are 13 cm and 8 cm. AB is the diameter of the bigger circle touching it at D. Find find length of AD.​

Answer 1

join AD and AE

proof - in triangle ODE

(by pyathgoras therom)

OD²=OB²-OD²

DB²=(13)²-(8)10

DB=/105

ED=/105 (as perpendicular OD from the centre of the circle O ,to a chord ED bisect the chord )

in triangle AEB

LAEB =90° ( as angle one semi circle is a right angle )

OD//AE

OD=1/2 AE ( segment joining the mid point of any 2 sides of a traingle is // to the third side also half of it )

AE= 16

in triangle AED

AD²= 16²+(105root)²

AD²= 256+105

AD²=361root

AD=19 ✓