Question

13) If four tangents of a circle determine a rectangle, then show that it
must be a square.​

Answer 1

Answer:

Step-by-step explanation:

If 4 tangents of a circle determine a rectangle,

Here ABCD is rectangle. Circle with Center O is created touching point XLYM. These are points at which tangent touches.

A     L      B

X    O      Y

D    M      C

XY = AB = DC --SInce XY is parallel to AB and DC. Since X and Y are tangent points.

LM = AD = BC --Since LM is parallel to AD and BC. Since L and M are tangent points.

Now,XY = LM equal to diameter of Circle.

So AB = DC = BC = AC and AD and all 4 angles are 90 degree.

So ABCD is square.