Question

ABCD are the four consecutive points on a circle such that a b is equals to CD prove that AC is equals to BD​

Answer 1

Answer:

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Answer 2

AC = BD

Step-by-step explanation:

ABCD are the four consecutive points on a circle

AB = CD

Let AC  and BD are intersect at O

we know that angles in the same segment are equal

then,

$\angle DCA = \angle DBA ..(1)$

$\angle CDB = \angle CAB ..(2)$

in $\bigtriangleup AOB$ and $\bigtriangleup DOC$

$\angle OAB = \angle ODC$

AB = CD (given)

$\angle OCD = \angle OBA$ (from 2)

thus

$\bigtriangleup AOB \cong \bigtriangleup DOC$ (by ASA congruency rule)

AO= DO ...(3)

and

BO= C0 ..(4)

adding (3) and (4)

we get,

AO+C0 = D0 +BO

AC = BD

hence proved .

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