Question

Hy !! here's one question for you all !! prove that theorem ..... please help me

Answer 1

$\huge\mathfrak {Answer:-}$

$Given:-$

X, Y and V are three non-collinear points.

$To \:prove:-$

There is one and only one circle passing through X, Y and V.

$Construction:-$ 

Join XY and YV.

Draw the perpendicular bisectors TZ and SW of the chords XY and YV respectively.

Let SW and TZ intersect at O.

Joint OX, OY and OV.

$Proof:-$

O lies on the perpendicular bisector of XY.

∴ $OX = OY$

Again, O lies on the perpendicular bisector YV.

∴ $OY = OV$

Thus,

$OX = OY = OV$ = r 

Taking O as centre, draw a circle of radius r.

V (0, r) passes through X, Y and V.

Thus,

A circle passes through the point X, Y and V.

If possible, suppose there is another circle with centre O' and radius r, passing through X, Y and V.

Then, O' will lie on the perpendicular bisector SW and TZ.

We know that,

2 lines cannot intersect at more than one point.

So,

O' must coincide with O.

Hence,

There is one and only one circle passing through three non collinear points.

$\huge{Be\:Brainly}$❤️