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# Question 18. (a) In the figure (i) given below, PA and PB are tangents at a points A and B respectively of a circle with centre O. Q and R are points on the circle. If ∠APB = 70°, find (i) ∠AOB (ii) ∠AQB (iii) ∠ARB (b) In the figure (ii) given below, two circles touch internally at P from an external point Q on the common tangent at P, two tangents QA and QB are drawn to the two circles. Prove that QA = QB.

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This is circle based question from Chapter name- circles
Topic – Angle properties of circles
Chapter number- 15

In first part of question it is given that, PA and PB are tangents at a points A and B respectively of a circle with centre O. Q and R are points on the circle.

If ∠APB = 70°, now we have to  find (i) ∠AOB (ii) ∠AQB (iii) ∠ARB

In second part , given that two circles touch internally at P from an external point Q on the common tangent at P, two tangents QA and QB are drawn to the two circles.

Now we have to prove that QA = QB.

ICSE Avichal publication
Understanding ICSE Mathematics
Question no 18

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### 2 Answers

1. Solution:
(a) To find : (i) ∠AOB, (ii) ∠AQB, (iii) ∠ARB
Given: PA and PB are tangents at the points A and B respectively
of a circle with centre O and OA and OB are radii on it.
∠APB = 70°
Construction: Join AB

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2. Num b

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