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Question 2. (a) In the figure (i) given below, O is the centre of the circle. If ∠AOC = 150°, find (i) ∠ABC (ii) ∠ADC.

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

We have that O is the centre of the circle. If ∠AOC = 150°,we have to find

(i) ∠ABC

(ii) ∠ADC.

ICSE Avichal publication
Understanding ICSE Mathematics
Question no 2(a). Exercise 15.2


1 Answer

  1. Given,
    ∠AOC = 150° and AD = CD

    We know that an angle subtends by an arc of a circle

    at the center is twice the angle subtended by the same arc

    at any point on the remaining part of the circle.

    (i) ∠AOC = 2 × ∠ABC

    ∠ABC = ∠AOC/2 = 150o/2 = 75o

    (ii) From the figure, ABCD is a cyclic quadrilateral

    ∠ABC + ∠ADC = 180o

    (Sum of opposite angels in a cyclic quadrilateral

    Is 180o)

    75o + ∠ADC = 180o

    ∠ADC + 180– 75o

    ∠ADC = 105o

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