Question

Abcd is a quadrilateral in which ad =bc and angle adc=angle bcd. show a,b,c,d,are concyclic

Answer 1

Answer:

Step-by-step explanation:

ABCD is a quadrilateral in which AD=BC and ∠ADC = ∠BCD.

To prove : ABCD lies on a circle i.e they are concyclic.

Join AC and BD .

Now in ∆ADC and ∆BDC,

AD = BC (given)

∠ADC =∠BDC (given)

DC= DC (common)

∆ADC≅∆BDC ( SAS congruency)

∠DAC =∠DBC ( by CPCT )

Hence the angle made by a segment on the other part of the circle are equal.

Hence A,B,C,D must lie on a circle.

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Answer 2

ABCD is a quadrilateral in which AD-BC and ZADC =

<BCD.

To prove : ABCD lies on a circle i.e they are

concyclic.

Join AC and BD.

Now in AADC and ABDC,

AD BC (given)

ZADC=2BDC (given)

DC DC (common)

AADC ABDC (SAS congruency)

<DAC=2DBC (by CPCT)

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