Question

in the figure ab is equal to CD prove that x is equal to y tommorow is my paper plz answer it plzzzzzzz​

Answer 1

Hello mate,

$\huge{\star} {\red{\huge{Solution}}} \huge{\star}$

We know that line segments OA, OB, OC, and OD are the radii of the circle.

So, OA = OB = OC = OD.

Now we need to prove angle X = angle Y

For both the angles to be equal, AC and BD should be equal.

This is because If we see in triangle OAC and OBD,

OA = OB

And if AC = BD, then both triangles will be isoceles and angle x and y will be equal.

Now let's prove how both are equal:

Let's suppose both AC and BD are equal, as we already know OA = OB,

OA + AC = OB + BD

OA + AC = OA + BD

(OA = OB so both get canceled)

(Check diagram for better understanding)

Hence, AC = BD

Now we got both our required equations,

• OA = OB

• AC = BD

So the triangles OAC and OBD are isoceles and thus, as per Side Angle Side (SAS) property of congruence of triangles, angle X = angle Y

Hope it helps:)

Answer 2

Answer:

SAS CRITERION of CONGRUENCY will be applicable

Step-by-step explanation:

Given that

AB = CD

we know that equal chords subtends equal angle on centre.

Thus

$\angle \: AOB \: = \angle \: COD \: ...eq1\:$

Now in triangle AOC and BOD

AO=BO (Radius of circle)

OC=OD (Radius of circle)

$\angle \: AOC = \angle \: AOB + \angle \: BOC \: ...eq2 \\ \\ \angle \: BOD = \angle \: COD + \angle \: BOC \: ...eq3$

from eq1 we know that angle AOB = angle COD

and an equal angle BOC is added into both equal angles.

(when equals added to equals resultant will be equal)

Thus

$\angle \: AOC= \angle \: BOD$

Thus by SAS CRITERION of CONGRUENCY

$\triangle \: AOC \cong \: \triangle \: BOD$

Thus by CPCT

$\angle OAC = \angle OBD \\ \\ \angle x = \angle y$

Hence proved.