Question

I have doubt in this:​

Answer 1

Join OA and OC.

We know that tangent to a circle is always perpendicular to its radius at the point of contact.

So, OA perpendicular to DA and OC perpendicular to DC.

In quad,  AOCD,

∠ADC + ∠DAO + ∠DCO + ∠AOC = 360°  

=> 50° + 90° + 90° + ∠AOC = 360°

=> 230° + ∠AOC = 360°

=> ∠AOC = 130°

Now, reflex ∠AOC = 360° - ∠AOC  

= 360° - 130°

= 230°.

We know that angle subtended by an arc at the centre is double the angle subtended by the same arc at any point on the circle.

So, reflex ∠AOC = 2∠APC

=> ∠APC = 230°2

=> 115°

Hope it helps!

Answer 2

Answer:

Join here OA and OC.

Now DA and DC are tangents,then OA perpendicular to DA and OC perpendicular to DC.

In quadric ADCO,

<ADC+<OAD+<OCD+<AOC =360°

or, 50°+90°+90°+<AOC =360°

or, 230°+<AOC =360°

or, <AOC =360°-230°

So, <AOC =130°

So, reflex <AOC =360° -130°

=230°

Then,<AOP =230°/2

So, <AOP =115°

Hope it helps you ❤❤❤