Question

please answer in simplest way​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

In Δ PQT,

∠TPQ + ∠TQP + ∠Ф = 180 ( ANGLE SUM PROPERTY )..........I

Tangents are always ⊥ to radius at pt of contact

So ∠OPT = 90

∠ OPQ + ∠TPQ = 90.........................II

TP = TQ ( Tangents from point are equal )

So ∠ TPQ = ∠TQP ( Opposite angles of equal sides )...III

So in I

2 ∠ TPQ = 180 - Ф ( By III )

∠TPQ = 90 - 1/2 Ф................. IV

∠OPQ = 90 - ∠TPQ ( By II )

∠OPQ = 1/2 Ф ( By IV )

∠OPQ = 1/2 ∠PTQ

2 ∠OPQ = ∠PTQ

Hence Proved