In figure 3.79, O is the centre of the circle and B is a point of contact. seg OE seg AD, AB = 12, AC = 8, find

(1) Given AB = 12 , AC = 8
AB is the tangent . AD is the secant.
AC×AD = AB² [Tangent secant theorem]
8×AD = 12²
AD = 144/8 = 18
Hence measure of AD is 18 units
(2) AD = AC+DC [A-C-D]
18 = 8+DC
DC = 18-8
DC = 10
Hence measure of DC is 10 units.
(3) Given OEAD
OECD [A-C-D]
DE = ½ CD [Perpendicular from centre of circle to chord bisects the chord]
DE = ½ ×10
DE = 5
Hence measure of DE is 5 units.