Prove that the quadrilateral formed by internal angle bisectors of a cyclic quadrilateral is also cyclic.
Given that: ABCD is a cyclic quadrilateral
To Prove: EFGH is also cyclic quadrilateral.
Proof:
ABCD is a cyclic quadrilateral and we know that the sum of the opposite angles of a cyclic quadrilateral is.
So,
Now,
…… (1)
Now,
In
…… (2)
And
…… (3)
Adding equation (2) and (3), we have,
Substitute value of from equation (1), in above equation, we have,
The sum of opposite angles of a quadrilateral is.
Hence, EFGH is a cyclic quadrilateral.