In the given figure, X and Y are centers of

ahiahysel

ahiahysel

Answered question

2022-03-01

In the given figure, X and Y are centers of two intersecting equal circle. If XY=AB, prove that AXBY is a square.

Answer & Explanation

vzletanje8z0

vzletanje8z0

Beginner2022-03-02Added 6 answers

Step 1
It is given that X and Y are the centers of two intersecting equal circles by which we can say that the radius of both circles is equal.

Two circles are equal if they have the same radius.
Also, it is given that XY=AB
To Prove: AXBY is a Square
Step 2
Proof
Since the radius are equal Therefore we can say that
AX=AY=BY=XB
Since all the sides are equal to a quadrilateral and also the diagonals
XY=AB
Again,
In AXB and
AX=AY (radius of same circle)
BX=BY (radius of same circle)
XY=AB (given)
Therefore, By SSS (Side-Side-Side) congruence rule
AXB=AYB
By CPCT
AXB=AYB
We know the sum of the opposite angles of a quadrilateral is, Therefore, we have,
AXB+AYB=180
2AXB=180
AXB=90
Similarly,
AXB=XBY=BYA=XAY=90
Step 3
All the sides of the quadrilateral AXBY are equal.
Diagonals of the quadrilateral AXBY are equal.
All angles of the quadrilateral AXBY are 90
Hence AXBY is a square
Hence Proved.

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