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:

Draw circle O and mark points A & B on it (I suggest such that central angle AOB is around 30 to 60 degrees.

Elsewhere, marks points C & D on the circle with central angle COD equaling angle COD.  The arrangement of points on the circle will be such that you go from A to B to C to D by moving clockwise around the circle.

 

Then equal chords AB & CD have equal arcs AB & CD.

 

Note that arc ABC will equal arc BCD, because arc AB + arc BC = arc BC + arc CD.

 

The chords of arc ABC & arc BCD will therefore be equal ("equal arcs have equal chords, on a given circle").

 

Therefore AC = BD.

Answer 2

AC = BD

Step-by-step explanation:

given that : ABCD are the four consecutive points on a circle and AB = CD

prove : AC = BD

solution:

let AC and BD intersect at point O .

we know that the angles in the same segment are equal .

$\angle DCA = \angle DBA ...(1)\\\angle CDB = \angle CAB..(2)$

Now in

$\bigtriangleup AOB and \bigtriangleup DOC\\\angle OAB = \angle ODC (from 1)\\AB = CD \\\angle OCD= \angle OBA (from 2)\\Thus,\\\bigtriangleup AOB \cong \bigtriangleup DOC$

by ASA congruency rule.

AO = DO ...(3)

BO = C0 ..(4)

Adding 3 and 4

AO + CO = DO+BO

AC = BD

hence , AC = BD

#Learn more:

in a parrallelogram abcd,e is a p oint on ab , such t hat ce b isects b cd . If ed = ae an d bc =4 , find be

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