Question

The bisectors at opposites $\angle s$ A and C of a cyclic quadrilateral ABCD intersect the circle at E and F respectively. Prove that EF is a diameter of the circle

• A. undefined
• B. undefined
• C. undefined
• D. undefined

Answer 1

In order to prove EF is diameter we used to prove $\angle ECF={90}^{\circ }$
$\angle ECF=\angle ECB+\angle BCF$
$=\frac{1}{2}\hat{C}+\angle EAB(\because \angle BCF\&\angle$ EAB are angles is same segment of E B)
$=\frac{1}{2}\hat{C}+\frac{1}{2}\hat{A}=\frac{1}{2}(\hat{C}+\hat{A})=\frac{1}{2}={180}^{\circ }={90}^{\circ }$
$\therefore$ EF is a chard.