Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Geometry

Question:

In a circle, AB and CD are two diameters which are perpendicular to each other. Find the length of chord AC.

Options:

$\sqrt{2}$ CD

$\frac{AB}{\sqrt{2}}$

$\frac{CD}{2}$

2AB

Correct Answer:

$\frac{AB}{\sqrt{2}}$

Explanation:

In triangle AOC ,

h² = b² + p²

AC² = OA² + OC²

{ OA = OC  = Radius of circle }

AC² = OA² + OA²

AC² = 2OA²

AC² = 2 × (\(\frac{AB}{2}\))²

AC² =  \(\frac{AB²}{2}\)

AC = \(\frac{AB}{√2}\)