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Question

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

A
17 cm
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B
15 cm
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C
4 cm
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D
8 cm
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Solution

The correct option is D 8 cm
OX is the perpendicular distance from centre O to the chord AB
AX=XB
Now,
AX+XB=AB
2AX=AB
2AX=30
AX=302
AX=15
Again,
AO+OD=AD
2AO=AD
2AO=34
AO=17
AOX is a right angled triangle
AO2=OX2+AX2
172=OX2+152
OX2=172152
OX2=64
OX=8cm

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