A 15 cm long perpendicular is drawn from the centre of a circle to its 40 cm long chord Find t...........

Quantitative Aptitude (CGL) Geometry

A 15 cm long perpendicular is drawn from the centre of a circle to its 40 cm long chord. Find the radius of the circle.

This questions was previously asked in

Combined Graduate level Examination 2023 Tier I

25 cm

27 cm

22 cm

20 cm

- A perpendicular from the center of a circle to a chord bisects the chord.

- Chord length = 40 cm, so each half is 20 cm.

- A right triangle is formed with the radius as the hypotenuse, half the chord as one leg, and the perpendicular as the other leg.

- Use the Pythagorean theorem: \((\text{radius})^2 = (\text{perpendicular})^2 + (\text{half of chord})^2\).

- Substitute values: \((\text{radius})^2 = 15^2 + 20^2\).

- Calculate: \((\text{radius})^2 = 225 + 400 = 625\).

- Radius = \(\sqrt{625} = 25\) cm.

- Option 1: 25 cm is correct.

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