Question

please answer me with proof.
as soon as possible​

Answer 1

Step-by-step explanation:

Given :-

• PQ is a tangent of a circle
• OP is a radius of a circle

To find :-

• ∠POQ

Solution :-

➤ For better understanding please refer to attachment

We know that,

Tangent is perpendicular to radius

∴ ∠OPQ is 90°

Since ∆OPQ is isosceles

➭ OP = PQ

$\\ {\bold{\bf{\fbox{Isosceles triangle property :-}}}}$

✏ Opposite sides of an isosceles triangle are equal as well as their angles

Therefore,

∠OQP = ∠ POQ

Thus,

${\bold{\sf{∠ POQ \: \: = \: \: \frac{1}{2} \: × \: 90°}}}$

${\bold{\sf{\fbox{\pink{∠ POQ \: = \: 45°}}}}}$