Question

In the given figure, if PQR is a tangent to the circle at Q whose Centre is O and AB is a chord Parallel to PR such that ∠BQR=70°, then find ∠ABQ.
(Class 10 Maths Sample Question Paper)

Answer 1

Mistake in the question. we have to find ∠AQB.

FIGURE IS IN THE ATTACHMENT.

SOLUTION:
Given :

AB || PR  & LQ ⟂PR  [ OQ ⟂PR =  LQ ⟂PR]
LQ ⟂AB = OL ⟂ AB= OL bisect chord AB(AL = BL)

In ∆ ALQ & ∆ BLQ

AL = BL   [ proved above]
∠ALQ = ∠BLQ           [each angle is 90°]
LQ = LQ                       [ Common]
∆ ALQ ≅∆ BLQ             [SAS Criterion]

∠LQA = ∠LQB               [ By CPCT]

∠LQB = 90° - 70° = 20°
∠LQA = ∠LQB= 20°
∠AQB=∠LQA +∠LQB
∠AQB= 20° + 20 ° = 40 °

Hence , ∠AQB is 40°.

HOPE THIS WILL HELP YOU...

Answer 2

HELLO DEAR,

PQR is a tangent
AB II PR
angle BQR = 70
so ∠BAQ = ∠BQR = 70 ( alternate angles)
and ∠ABQ = ∠BQR = 70 ( as AB II PR)

by summing all the angles 
∠BAQ + ∠ABQ +∠AQB= 180
∠AQB = 180 - 70 -70
= 40 

I HOPE ITS HELP YOU DEAR,
THANKS