Question

plzz solve 7 question

Answer 1

proved 2angle 3=angle5

Answer 2

Answer:

Here, Tangents PT and PQ are drawn from an external point P to a circle with center O,

Since, TO and QO are the radius of the circle,

⇒ TO = OQ,

⇒ Δ TOQ is an isosceles triangle,

∠ OTQ = ∠ OQT  

Also,  ∠OTP = ∠OQT = 90°

⇒ ∠90° - ∠QTP = 90° - ∠TQP

⇒ ∠QTP = ∠TQP ----(1),

In triangle PTQ,

∠TPQ + ∠ QPT + ∠ TQP = 180°

⇒ ∠TPQ = 180° - (∠TPQ + ∠ QPT) = 180° - 2∠QTP = 180° - 2(90°-∠OTQ ) = 2∠OTQ ( Because, ∠QTP = 90° - ∠OTP )

Thus, ∠TPQ = 2∠OTQ

Hence, proved.