Previous Year Questions

Given XY=11 cm

YZ=13 cm

XZ=24 cm

Formula used:-

For three points to lie on a circle, the sum of the lengths of any two sides must be greater than the length of the third side.

Calculation

Checking the triangle inequality for the given lengths:

XY + YZ > XZ

11 + 13>24 (not true)

XY + XZ > YZ

11 + 24> 13 (true)

YZ + XZ> XY

13 + 24>11 (True)

As one of them is "not true", Points X,Y,Z do not form a valid triangle and hence do not lie on a circle.

So the number of circles that can pass through points X,Y and Z is zero.

Option (a) is the correct answer.