This is an important and exam oriented question from Chapter name- circles

Topic – Angle properties of circles

Chapter number- 15

ICSEIn this question we have figure of circles with constructions and we have to find the value of x using basic properties of circles.

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Understanding ICSE Mathematics

Question2

Arc AB subtends ∠AOD at the centre and ∠ACD at the remaining part of the Circle

∠AOD = 2 ∠ACB

∠ACB = ½ ∠AOD = ½ × 70

^{o }= 35^{o}∠CMO = 90

^{o}∠AMC = 90

^{o}(∠AMC + ∠CMO = 180

^{o})Now in ∆ACM

∠ACM + ∠AMC + ∠CAM = 180

^{o}35

^{o}+ 90^{o }+ x^{o }= 180^{o}125

^{o }+ x^{o }= 180^{o}X

^{o }= 180 – 125^{o }= 55^{o}