Question

ABCD is a cyclic quadrilateral.if AC bisect both the angles A and C then prove that angle ABC=90 degree.

Answer 1

In the triangles ABC & ADC
∠BAC=∠DAC
∠DCA=∠BCA
AC=CA
ΔABC & ΔADC are congruent
∠CDA=∠ABC
∠CDA+∠ABC=180°(opposite angle of a cyclic quadrilateral are supplementary)
2ABC=180°
∠ABC=180/2
∠ABC=90° 

Answer 2

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