In a circle of $10$ cm radius, two chords $A B = A C = 12 c m$ , then the length of the chord $B C$ is?

12

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9.6

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19.2

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7.2

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Solution

The correct option is B $19.2$ cm
In $Δ$ OBM $10^{2} = (O M)^{2} + x^{2}$ ....... $(1)$ In $Δ$ ABM $12^{2} = x^{2} + (10 - 0 m)^{2}$ ........ $(2)$
Eq $(2) -$ Eq. $(1)$
$144 - 100 = x^{2} + 100 + O M^{2} - 20 \times O M - x^{2}$
$44 = 144 - 20 \times O M \Rightarrow O M = 2.8$
Put $O M = 2.8$ in Eq. $(1)$
We get $x = 9.6$ , so BC $= 2 \times 9.6 = 19.2$ .

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In a circle of 10cm radius, two chords AB=AC=12 cm, then the length of the chord BC is?

The correct option is B 19.2cmIn ΔOBM 102=(OM)2+x2 .......(1)In ΔABM 122=x2+(10−0m)2 ........(2)Eq(2)−Eq.(1)144−100=x2+100+OM2−20×OM−x244=144−20×OM⇒OM=2.8Put OM=2.8 in Eq. (1)We get x=9.6, so BC=2×9.6=19.2.

In a circle of $10$ cm radius, two chords $A B = A C = 12 c m$ , then the length of the chord $B C$ is?