Question

In a circle with centre O, AB and CD are two diameters perpendicular to each other. The length of chord AC is

(a) 2AB

(b) $\sqrt{2}$

(c) $\frac{1}{2}AB$

(d) $\frac{1}{\sqrt{2}}AB$

Answer 1

(d) $\frac{1}{\sqrt{2}}AB$

We are given a circle with centre at O and two perpendicular diameters AB and CD.

We need to find the length of AC.

We have the following corresponding figure:

Since, AB = CD (Diameter of the same circle)

Also, ∠AOC = 90°

And, AO =

Here, AO = OC (radius)

In ΔAOC

Hence, the correct answer is option (d).