Question

AB is a chord of a circle with centre P. point C is a point other than A and
B on major arc AB. Answer the following questions.

answer the marked question
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Answer 1

Answer:

Step-by-step explanation:

(a) As shown in the fig

∠APB=2*∠ACB

=2*50=100°

b) ∠ACB=1/2*∠APB

=130/2=65°

Answer 2

Step-by-step explanation:

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Given, ∠AOB=110∘

In △AOB

OA=OB (Radius of the circle)

Thus, ∠OAB=∠OBA (Isosceles triangle property)

Sum of angles of the triangle = 180

∠AOB+∠OAB+∠OBA=180

110+2∠OBA=180

∠OBA=35∘

Since, PQ is a tangent touching the circle at B.

Thus, ∠OBQ=90∘

Now, ∠ABQ+∠OBA=90

∠ABQ+35=90

∠ABQ=55°

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