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# Question 6. (a) In the figure (i) given below, O is the centre of the circle and ∠PBA = 42°. Calculate the value of ∠PQB (b) In the figure (ii) given below, AB is a diameter of the circle whose centre is O. Given that ∠ECD = ∠EDC = 32°, calculate (i) ∠CEF (ii) ∠COF.

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This is the basic and conceptual question from Chapter name- circles
Topic – Angle properties of circles
Chapter number- 15

In this question we have been given the figure of circle with certain information about the figure and we have to find <PQB im first figure, and <CEF, <COF in second figure

ICSE Avichal publication
Understanding ICSE Mathematics
Question 6

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1. Solution:

In ∆APB,

∠APB = 90° (Angle in a semi-circle)

But ∠A + ∠APB + ∠ABP = 180° (Angles of a triangle)

∠A + 90° + 42°= 180°

∠A + 132° = 180°

⇒ ∠A = 180° – 132° = 48°

But
∠A = ∠PQB

(Angles in the same segment of a circle)

∠PQB = 48o

(b) (i) in ∆EDC,

(Ext, angle of a triangle is equal to the sum

of its interior opposite angels)

(ii) arc CF subtends ∠COF at the centre and

∠CDF at the remaining part of the circle

∠COF = 2 ∠CDF = 2 ∠CDE

=2 × 32= 2 ∠CDE

= 2 × 32= 64o

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