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*ABC* is a triangle with *B* as right angle, *AC *= 5 cm and *AB* = 4 cm. A circle is drawn with* A*as centre and *AC *as radius. The length of the chord of this circle passing through *C* and *B* is

#### Options

3 cm

4 cm

5 cm

6 cm

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#### Solution

6 cm

We are given a right triangle *ABC* such that `angleB ` = 90° , *AC* = 5 cm, *AB* = 4 cm. A circle is drawn with *A* as centre and *AC* as radius. We have to find the length of the chord of this circle passing through *C* and *B*. We have the following figure regarding the given information.

In the circle produce *CB* to *P*. Here *PC* is the required chord.

We know that perpendicular drawn from the centre to the chord divide the chord into two equal parts.

So, *PC* = 2*BC*

Now in Δ*ABC* apply Pythagoras theorem

`BC^2 = AC^2 - AB^2`

`=5^2 - 4^2`

= 25 - 16

= 9

BC = 3 cm

So, *PC *= 2 ×* BC*

= 2 × 3

= 6 cm

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