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Sum of Trigonometric Ratios in Terms of Their Product

In Fig. 3 if ...

Question

In Fig. 3 if $O A = 5 c m a n d O M = 3 c m$ , the length of chord AB (in cm) is

A

8

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B

10

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C

6

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D

4

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Solution

The correct option is A 8
Given $O A = 5 C M$
$O M = 3 C M$
$∠ O M A = ˚ 90$
So by Pythagoras theorem,
${A M}^{2} = {O A}^{2} - {O M}^{2}$
${A M}^{2} = 5^{2} - 3^{2}$
$A M = 4 c m$
We know that perpendicular from centre bisects the chord
Therefore $A B = 2 A M$
$A B = 8 c m$

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