Question

AB and CD are two chords such that AB = CD. If chord AB subtend an angle of 45° at the centre of the circle, then find the angle subtended by chord CD at the centre of the circle.​

Answer 1

Answer:

Nothing to answer:

12+34+45=91 degree

Answer 2

Given:

AB and CD are two chords such that AB = CD. If chord AB subtend an angle of 45° at the centre of the circle,

To Find:

find the angle subtended by chord CD at the centre of the circle.​

Solution:

If there are two equal chords and one of the subtends angle theta at the centre of the circle then the other chord will also subtend the same angle theta and both chords are also equidistant from the centre. So the chord CD will also subtend an angle of 45 degrees. We can also prove this statement by the congruency of triangles,

Construct a circle and draw two equal chords and name the length as 'a', now join both the ends of both chords with the centre of the circle now we have two triangles ABO and CDO,

From the data and the figure, we can conclude some points as,

AB=CD

CO=AO

DO=BO

So from SSS(side side side ) congruency, both the triangles are congruent to each other,

$\bigtriangleup ABO\cong \bigtriangleup CDO$

So, now because both the triangles are congruent to each other then we can say that

$\angle AOB =\angle COD=45^{\circ}$

Hence, the angle subtended by chord CD at the centre is 45 degrees.