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AD is a diameter of a circle and AB is a...

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

A

`17` cm

B

`15` cm

C

`4` cm

D

`8` cm

Text Solution

Verified by Experts

The correct Answer is:
D
Given, AD = 34 cm and AB = 30 cm
In figure, draw `OLbotAB`.
Since, the perpendicular from the centre of a circle to a chord bisects the chord.

`:.AL=LB=1/2 AB=15cm`
`"In right angled "DeltaOLA, OA^(2)=OL^(2)+AL^(2) "[by pythagoras theorem]"`
`:.(17)^(2)=OL^(2)+(15)^(2)`
` Rightarrow289=OL^(2)+225`
`Rightarrow OL^(2)=289-225=64`
`:. OL=8 cm`
[taking positive square root, because length is always positive]
Hence, the distance of the chord from the centre is 8 cm.
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