Mathematics
AB and CD are two parallel chords of a circle of lengths 10 cm and 4 cm respectively. If the chords lie on the same side of the centre and the distance between them is 3 cm, find the diameter of the circle.
Circles
ICSE
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Answer
Let OE = x cm.
From figure,
![AB and CD are two parallel chords of a circle of lengths 10 cm and 4 cm respectively. If the chords lie on the same side of the centre and the distance between them is 3 cm, find the diameter of the circle. Circle, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.](https://cdn1.knowledgeboat.com/img/mla9/q9-c15-ex-15-1-circle-ml-aggarwal-solutions-icse-class-9-1057x1025.png)
In right angle triangle OCF,
⇒ OC2 = OF2 + CF2 (By pythagoras theorem)
⇒ OC2 = (x + 3)2 + 22
⇒ OC2 = x2 + 9 + 6x + 4
⇒ OC2 = x2 + 6x + 13
Since, radius = OA = OC.
∴ OA2 = OC2 = x2 + 6x + 13.
In right angle triangle OAE,
⇒ OA2 = OE2 + AE2
⇒ x2 + 6x + 13 = x2 + 52
⇒ x2 - x2 + 6x = 25 - 13
⇒ 6x = 12
⇒ x = = 2 cm.
⇒ OC2 = x2 + 6x + 13
⇒ OC2 = 22 + 6(2) + 13
⇒ OC2 = 4 + 12 + 13
⇒ OC2 = 29
⇒ OC = cm.
Diameter = 2 × radius = 2 × cm.
Hence, diameter = cm.
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