Question

In a circle with centre O, AB and CD are two diameters perpendicular to each other. Find the

length of chord AC.​

Answer 1

Hi,

Since the measurements are not given we will take the sides as as it is.

Now, it is given AB perpendicular to CD.

therefore , <cod = 90deg

Since AB PERPENDICULAR TO CD .

Join AC , OA=OC (radii)

In triangle , AOC

AC^2 = OA^2+OC^2

AC= ROOT of OA +OC

Hope the ans is correct !!

Answer 2

AB and CD bisect each other at point O in a circle ...1

also AB =CD ...(since AB and CD are diameters of circle )...2

from equation 1

AO =CO=BO=DO

Let, AO=CO=BO=BO=x

in ∆AOC angleAOC =90°

Therefore by pythagoras theorem

AC^2=CO^2+AO^2

=x^2+x^2

=2x^2

taking square root on both side

AC=√2x