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Question

Question 1
AD is a diameter of a circle and AB is a chord. If AD = 34cm, AB = 30cm, the distance of AB from the centre of the circle is


(A) 17 cm
(B) 15 cm
(C) 4 cm
(D) 8 cm

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Solution

(D) 8 cm

Given, AD = 34 cm and AB = 30 cm
Consider the figure given below,


Draw OL AB
Since the perpendicular from the centre of a circle to a chord bisects the chord,
AL=LB= 12 AB=15cm

In right angled Δ OLA,
OA2=OL2+AL2
(17)2=OL2+(15)2
289=OL2+225
289=OL2+225
OL2=289225=64
OL=8cm
[taking positive square root, because lentgh is always positive]
Hence, the distance of the chord from the centre is 8cm.


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