Question

please solve this asap​

Answer 1

Answer:

A) 50°

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Answer 2

Answer:

∠POA = 50°

Step-by-step explanation:

Given,

If tangents PA and PB from a point P to a circle with center O are inclined to each other at angle of 80°.

To Find:

∠POA = ?

Solution:

In ΔPOA and ΔPOB,

==> ∠POA = ∠PBO

==> OA = OB(radii of circle)

==> OP = OP(Common)

∴ ΔPOA ≅ ΔPOB[SSS congruency]

==> ∠OPA = ∠OPB

==> ∠OPA = ∠OPB = 40°

In ΔPAO,

∠APO + ∠POA + ∠OAP = 180°

==> 40° + ∠POA + 90° = 180°

==> ∠POA = 180° - 130°

==> ∠POA = 50°

Result:

∠POA = 50°