Question

prove that

equal cords of a circle susbtend equal angles at a centre ​

Answer 1

Given :-

A circle with radius r and center o

Chord AB = Chord CD

To prove :-

Angle AOB = Angle COD i.e,

Angle 1 = Angle 2

Proff :-

In Triangles AOB and COD

AO = CO [ As radii of same circle ]

OB = OD [ As radii of same circle ]

AB = CD [ Given ]

∴ By SSS Congrency

Triangle AOB is congrent to Triangle COD

$\: \sf\bold{\blue{∴ Angle \: 1 = Angle \: 2 \: [ By C.P.C.T ] }}$

So,

Angle AOB = Angle COD

Hence proffed

Note :-

• Figure is attachment

We know :-

• SSS (Side-Side-Side)

If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.