Question

in the figure, PA and PB are tangents to the circle with Centre O. if angle OAB=25° then find the angle APB

Answer 1

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Answer 2

Answer: The value of angle APB is 50°.

Step-by-step explanation:

Since we have given that

PA and PB are tangents to the circle with centre O.

∠OAB = 25°

As shown in the figure:

AS we know that

∠PAO = 90°

so, it becomes,

$\angle OAB+\angle PAB=\angle PAO\\\\25^\circ+\angle PAB=90^\circ\\\\\angle PAB=90-25=65^\circ$

Since PA = PB

And we know that equal sides have equal angles.

so. it becomes,

∠PAB=∠OBA=65°

Consider, ΔAPB,

$\angle APB+\angle PAB+\angle PBA=180^\circ\\\\\angle APB+65^\circ+65^\circ=180^\circ\\\\\angle APB=50^\circ$

Hence, the value of angle APB is 50°.