Question

pls help me with the answer

Answer 1

Answer:

20 degree

Step-by-step explanation:

We know that length of tangents drawn from an external point to a circle are equal

∴ TP=TQ−−−(1)

4∴ ∠TQP=∠TPQ (angles of equal sides are equal)−−−(2)

Now, PT is tangent and OP is the radius.

∴ OP⊥TP (Tangent at any point pf circle is perpendicular to the radius through the point that cant act)

∴ ∠OPT=90

or, ∠OPQ+∠TPQ=90

or, ∠TPQ=90 −∠OPQ−−−(3)

In △PTQ

∠TPQ+∠PQT+∠QTP=180

(∴  Sum of angles triangle is 180 )

or, 90  −∠OPQ+∠TPQ+∠QTP=180

or, 2(90  −∠OPQ)+∠QTP=180

 [from (2) and (3)]

or, 180 −2∠OPQ+∠PTQ=180

∴ 2∠OPQ=∠PTQ−−−− Put the value of PTQ and find out the answer