Question

two tangents are drawn from a point P to a circle at A and B .O is the centre of circle .if angle AOP is 60. then angle APB is.

Answer 1

Answer:

60 degrees

Step-by-step explanation:

As line AP id tangent to the circle with center O, therefore angle OAP will be 90 degrees.

angle AOP = 60 degrees (given), so,

angle APO = 180-( OAP +AOP) = 180 - (90 +60) = 180 - 150 = 30 degrees ..(1)

Here, we have two triangle, vis. OAP & OBP having a common hypotenuse OP with OB = OA (radius of the circle)

Hence, two triangles are congruent (by property of congruence using 'RHS') .

Therefore, angle(APO) = angle(BPO) = 30 degree ( from ..(1))

angle(APB) = angle(APO) + angle (BPO) = 30 +30 = 60 degrees. (Answer)