Question

Please solve this:
(fast plzz)

Answer 1

Given. PT is the tangent and PAB is a secant.
To Prove: PT2 = PA × PB

Construction: Draw seg BT and AT

Solution:In ∆ PTA and ∆ PBT∠ PTA ≅ ∠ PBT [Angles in alternate segment]∠ TPA ≅ ∠ TPB [Common angle]∴ ∆PTA ∼ ∆ PBT  [A – A test for similarity]
by CSST
PT=TA=PA
PB  BT  PT
∴PT=PA
  PB  PT
∴ PT2 = PA × PB
Hence Proved.