Question

If chords AB and CD of congruent circles subtend equal angles at their centres, then:​

Answer 1

Step-by-step explanation:

If chords AB and CD of congruent circles subtend equal angles at their centres, then their chords are equal.

Answer 2

Given:

We have Chords AB and CD of congruent circles subtend at equal angles at their centres.

To Find:

Possiblity of two chord?

Step-by-step explanation:

It is given to us that  two chords of congruent circles equal angles at the center.

We will show  the chords are equal.

Now the circles are congruent  we can have  the same one circle, just  a circle is always congruent to itself.

Let us consider two congruent circles.

Let the triangle be AOB and COD.

It is given that

angleAOB is equal to angle COD.………..(i)

We know that  radius of the congruent circles  equal, which gives,

OA = OC …..(ii)

Again, we have that radius of the congruent circles equal, which gives,

OB = OD………(iii)

Now we will use SAS congruence theorem which is stated as,

all the three conditions of SAS congruence rule are satisfied which is given by eqn (i), eqn (ii) and equation (iii).

Hence, by applying rule of SAS congruence in

Hence, both  above triangles are congruent.

Now  from CPCT states that

Then with  rule of CPCT the sides are equal, which will gives,

AB = CD, which was required to prove.

Hence, chord are equal in length.