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p is a point on AB if PA =PB then P is called the​

Answer 1

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Assume that P(A)=P(B). Prove that A=B.

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P(A)=P(B)

inorder to prove A=B, we should prove A is a subset of B i.e., A⊂B

and B is a subset of A i.e., B⊂A

Set A is an element of power et of A as every set is a subset

i.e., P∈P(A)

A∈P(B)

if set A is in power set of B

Set A is a subset of B

A⊂B

Similarly we can prove

B⊂A

Now since A⊂B and B⊂A

∴ A=B

Hence proved

Answer 2

Answer:

Yes: in fact, it can be done with any triangle. The point you’re looking for is the meeting point of the three perpendicular bisectors of the sides, AB, AC and BC. The perpendicular bisector of any line is the locus of points equidistant from its ends. So the point common to all three bisectors is equidistant from A, B and C.

It is the centre of the circle that goes through A,B and C, called the triangle’s circumcircle.

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