Question

abcd is a cyclic quadrilateral. if

Answer 1

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


Jasmin Cool asked in Math
ABCD is a cyclic quadrilateral.if AC bisect both the angles A and C then prove that angle ABC=90 degree.
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Tinker Bell answered this
35 helpful votes in Math, Class X
in triangleS ABC & ADC,

angle DAC = angle BAC (given)

angle DCA = angle BCA (given)

AC = CA (COMMON)

therefore, triangle ABC & triangle ADC are congruent

so angle CDA = angle ABC



angle CDA + angle ABC= 180 degree (opposite angle of a cyclic quadrilateral are supplementary)

2ABC=180 (since angle CDA = angle ABC)

ABC = 180/2

ABC = 90

PROVED