Question

. Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal. ​

Answer 1

Given:-

2 Congrent circles

circle with center o and radius r

circle with center o` and radius r`

Angle AOB = Angle CO`D

To prove:-

In triangles AOB and CO`D

AO= CO` ( radii of same circle)

Angle 1 = Angle 2 ( Given )

OB = O`D ( radii of same circle)

Therefore by SAS Congrency

Triangle AOB is congrent to Triangle CO`D

Therefore

AB = CD ( C.P.C.T)

So Chord AB = Chord CD

Hence proffed

Note:-

Figure in attachment

` it is just to differentiate between 2 circles

Now more:-

•Perimeter of circle is circumference of circle

Circumference = 2πr

• Chord :-

The line segment joining any two points on the circumference of the circle.