Question

ABCD is cyclic quadrilateral if AC bisect both the angels A and C then prove that angel ABC = 90° ​

Answer 1

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Answer 2

here is ur answer:

Given: ABCD is cyclic quadrilateral

To prove : angle ABC = 90°

Proof :

angle A + angle C = 180°..........{ sum of opp angles of cyclic quadrilateral is 180°}

$\frac{angle \: a}{2} + \frac{angle \: c}{2} = \frac{180}{2} \\ \\ \frac{angle \: a}{2} + \frac{angle \: c}{2} = 90$

since AC bisects angle A nd angle C

angle 1 = angle 2 = angle A/2

angle 3 = angle 4 = angle C/2

In ∆ABC

$angle \: 1 + angle \: 2 \: + angle \: b = 180 \\ \\ 90 + angle \: b = 180 \\ \\ angle \: b= 180 - 90 \\ \\ angle \: b = 90$

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