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प्रश्न
In the figure, given below, AB and CD are two parallel chords and O is the centre. If the radius of the circle is 15 cm, find the distance MN between the two chords of lengths 24 cm and 18 cm respectively.
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उत्तर
Given, AB = 24 cm, CD = 18 cm
⇒ AM = 12 cm, CN = 9 cm
Also, OA = OC = 15 cm
Let MO = y cm and ON = x cm
In right angled ∆AMO
(OA)2 = (AM)2 + (OM)2
⇒ 152 = 122 + y2
⇒ y2 = 152 – 122
⇒ y2 = 225 – 144
⇒ y2 = 81
⇒ y = 9 cm
In right angled ΔCON
(OC)2 = (ON)2 + (CN)2
⇒ 152 = x2 + 92
⇒ x2 = 152 – 92
⇒ x2 = 225 – 81
⇒ x2 = 144
⇒ y = 12 cm
Now, MN = MO + ON
= y + x
= 9 cm + 12 cm
= 21 cm
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