In the given figure, DX is a tangent. DX = OX = OC, if BX = 3cm and AB = 9 cm, then what is the value (in cm) of OD?

3 cm

DX² = XB × XA

DX² = 3  × [AB + BX]

DX² = 3 × [3 + 9]

DX² = 3 × 12 = 36

DX = 6 cm

CO = OX = DX = 6

∴ OB = OX - BX

= 6 - 3 = 3 cm

AO = AB - OB = 9 - 3 = 6 cm

AB and CD intersect at O,

AO × OB = CO × OD

6 × 3 = 6 × OD

OD = 3 cm