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Question
ABC is a triangle with B as right angle, AC = 5 cm and AB = 4 cm. A circle is drawn with Aas 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
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 = 2BC
Now in ΔABC 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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