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 - Mathematics

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MCQ

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

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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 = 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

  Is there an error in this question or solution?
Chapter 15: Circles - Exercise 15.7 [Page 110]

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RD Sharma Mathematics for Class 9
Chapter 15 Circles
Exercise 15.7 | Q 7 | Page 110

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