Question

A circle with centre of. Is in the exterior of the circle. line AP and AQ are tangents at the point P and Q respectively P-A-S,Q-A-R angle PAR= 130 degree. Find angle AOP​

Answer 1

Answer:

130 degree

half of 130 degree

Answer 2

Answer:

Step-by-step explanation:

< PAQ = 180' - < PAR..... angles in linear pair.

= 180' - 130'

= 50'

Now

In quandetrial OPAQ,

< OPQ = < OPA = 90' ......tangent theorem.

Now,

< OPA + < PAQ + < OQA + <POQ = 360'.....cyclic Quandetrial theorem.

90' + 50'+90'+ < POQ = 360'

230' + < POQ = 360'

< POQ = 130'

We have,

< POA = 1/2 < POQ.... given

Therefore,

< POA = 65'