3.   If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80 \degree, then \angle POA is equal to

      (A) 50°

      (B) 60°

      (C) 70°

      (D) 80°

Answers (1)
M manish

The correct option is (A)

It is given that,  tangent PA and PB from point P inclined at \angle APB = 80^0
In triangle \DeltaOAP and \DeltaOBP
\angle OAP = \angle OBP = 90
OA =OB (radii of the circle)
PA = PB (tangents of the circle)

Therefore, by  SAS congruence
\therefore \Delta OAP \cong \Delta OBP

By CPCT, \angle OPA = \angle OPB
Now, \angleOPA = 80/4 = 40

In \Delta PAO,
\angle P + \angle A + \angle O = 180
\angle O = 180 - 130
        = 50

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