Question

4. APB is tangent at P to the circle with centre 0. If angle
QPB = 60° then _POQ
(A) 120
B) 90°
(C) 100
(D) 600​

Answer 1

Answer:

A) 120° is the correct answer.

Step-by-step explanation:

according to the question, Q is a point on the circle.

angle OPB is 90° (being an angle on tangent)

given that angle QPB is 60°

so angle QPO is 90° -60° = 30°

angle QPO = angle PQO = 30°

therefore, Angle POQ = 180° - angle QPO - angle PQO

i.e. angle POQ = 180° - 30° - 30° = 120°

Answer 2

$answer -$

Given that:

∠QPB=60

∘

To find:

∠POQ=?

Solution:

∠QPB=∠QRP=60

∘

(Alternate segment theorem)

∠POQ=2∠QRP=2×60 =120

∘

(Angle subtended by the chord at the centre is twice of angle subtended by it at circumference.)

Hence, a is the correct option.