Short Answer Type
Long Answer TypeShort Answer Type5. In the given figure, find the values of a, b, c and d. Given that ∠BCD = 43° and ∠BAE = 62°.
Given: ABCD is a cyclic quadrilateral. AC bisects both the angles A and C.
To Prove: ∠ABC = 90°
Proof: In ∆ADC and ∆ABC,
∠DAC = ∠BAC
| ∵ AC bisects angle A
∠DCA = ∠BCA
| ∵ AC bisects angle C
AC = AC | Common
∴ ∆ADC ≅ ∆ABC
| ASA congruence rule
∴ ∠ADC = ∠ABC | CPCT
But ∠ADC + ∠ABC = 180°
| ∵ Opposite angles of a cyclic quadrilateral are supplementary
∴ ∠ADC = ∠ABC = 90°
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