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?
Answer & explanation
Correct answer: option 1
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