In the figure, XYZ is a secant and ZT is a tangent to the circle at T. If TZ = 12 cm and YZ = 8 cm, then find the length of XY.

10 cm

Concept Used

If PAB is a secant to a circle intersecting it at A and B and PT is a tangent then PA x PB = \( {PT }^{ 2} \)

Calculation

By using the above concept

ZX x XY = \( {ZT }^{ 2} \)

⇒ 8 x (YZ + XY) = \( {12 }^{ 2} \)

⇒ 8 x (8 + x) = 144

⇒ 8 + x = 18

⇒ x = 10 cm

Therefore, x is 10 cm.