急!急! F4 Properties Circles q2

20a) CD = QR (Equal distance from centre, equal chord length)

Also QN = NR (Radius perp. to chord bisects chord)

We have, QR = 10 cm, hence NR = 5 cm.

NS = RS + NR = 8 cm

b) PN = NS (Radius perp. to chord bisects chord)

Hence AN = AP + PN = 12 cm

22) Suppose that radius of the disc is r cm, then OD = (r - 2) cm

AD = DB = 9/2 = 4.5 cm (Radius perp. to chord bisects chord)

Using Pyth. thm:

OA^2 = AD^2 + OD^2

r^2 = 20.25 + (r - 2)^2

r^2 = 20.25 + r^2 - 4r + 4

4r = 24.25

r = 6.06