Mathematics
In the figure (ii) given below, CD is the diameter which meets the chord AB in E such that AE = BE = 4 cm. If CE = 3 cm, find the radius of the circle.
Circles
ICSE
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Answer
Given,
AB = 8 cm, EC = 3 cm
Let radius OB = OC = r
OE = (r - 3) cm.
Since, chord AB is bisected by OE so OE ⊥ AB (As straight line drawn from the centre of circle to bisect a chord, is perpendicular to it.)
Now in right ∆OBE,
⇒ OB2 = BE2 + OE2
⇒ r2 = 42 + (r – 3)2
⇒ r2 = 16 + r2 – 6r + 9
⇒ r2 - r2 + 6r = 16 + 9
⇒ 6r = 25
⇒ r = cm.
Hence, radius = cm.
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