Question

If tangents PA and PB drawn from an external point P to a circle with centre O are inclined to each other at an angle of 80°, then find ∠POA.

Answer 1

Given that, PA and PB are tangents.

∴ PA and PB are the tangents

∴ PO will be angle bisector of ∠P

Hence, ∠APO = 40°

Now, in ΔAPO,

∠P + ∠APO + ∠POA = 180°

90° + 40° + ∠POA = 180°

130° + ∠POA = 180°

∠POA = 180° – 130°

∠POA = 50°