Question

. A cyclic quadrilateral has three equal sides of length 36 cm with circum-radius 24 cm.
Then the length of the fourth side is ?

Answer 1

The length of the fourth side of the cyclic quadrilateral is $31.75cm$.

Given:

There is a cyclic quadrilateral with three equal sides of length $36cm$ each.

Its circum-radius $=24cm$

It is required to find out the length of the fourth side.

∴the circum-diameter

$=2*24\\=48cm$

The circum-diameter, the fourth side, and one of its equal length sides of the cyclic quadrilateral form a right-angled triangle with the circum-diameter as its hypotenuse.

Pythagoras' theorem states that in any right-angled triangle the square of the hypotenuse is equal to the sum of the squares of its other two sides.

Assume the length of the fourth side $=xcm$

$48^{2} =x^{2} +36^{2} \\x^{2} =48^{2} -36^{2} \\x^{2} =1008\\x=31.75cm$