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Question
Two chords of lengths 10cm and 24cm are drawn parallel o each other in a circle. If they are on the same side of the centre and the distance between them is 17cm, find the radius of the circle.
Solution
CP = PO = 12cm
Let OA = OC = r (say)
Also, let OQ = x, ∴ OP = 17 - x
In right Δ OPC,
By Pythagoras theorem,
OC2 = OP2 + PC2
r2 = (17- x)2 + 122 ----( 1 )
Similarly, In Δ OQA,
OA2 = AQ2 + QO2
r2 = 52 + x2 ----(2}
From (1) and { 2}
( 17 - x)2 + 122 = 52 + x2
289 - 34 x + 144 - 25 = 0
34x = 408
x = 12
From {2}
r2 = 52 + 122
25+ 144= 169
r = 13
The radius of the circle is 13cm .
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