## 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 = 8AB is the tangent . AD is the secant.AC×AD = AB2 [Tangent secant theorem]8×AD = 122AD = 144/8 = 18Hence measure of AD is 18 units(2) AD = AC+DC [A-C-D]18 = 8+DCDC = 18-8DC = 10Hence measure of DC is 10 units.(3) Given OEADOECD [A-C-D]DE = ½ CD […]

## In figure 3.78, chord MN and chord RS intersect at point D.

(1) Given RD = 15, DS = 4, MD = 8RD×DS = MD×DN [Theorem of chords intersecting inside the circle]15×4 = 8×DNDN = 15×4/8 = 60/8DN = 7.5 units(2) RS = 18, MD = 9, DN = 8RD×DS = MD×DN [Theorem of chords intersecting inside the circle](RS-DS)×DS = MD×DN [RD +DS = RS](18-DS)DS = 9×818DS […]

## In figure 3.77, ray PQ touches the circle at point Q. PQ = 12, PR = 8, find PS and RS.

Given PQ = 12 , PR = 8PQ is a tangent to the circle.PQ2 = PR ×PS122 = 8×PSPS = 144/8PS = 18PS = PR+RSRS = PS-PRRS = 18-8 = 10Hence PS = 18 units and RS = 10 units.