Question

In the figure arc AXB ≅ arc CYD. If AB = 6 cm
then find the length of chord CD

Answer 1

Answer:

Chord CD= 6cm

Step-by-step explanation:

In the figure,

Arc AXB ≅ arc CYD

In a circle the chords corresponding to congruent arcs are congruent

.°. chord AB = chord CD

.°. chord CD = 6cm

Answer 2

The length of the chord will be equal to 6 cm

Given:

$arc(AXB)$ ≅ $arc(CYD)$

$AB=6cm$

To find:

The length of the chord.

Solution:

We have been given that the $arc(AXB)$ is congruent to $arc(CYD)$ and we know that the length of the arc is given by,

$l=R\alpha$

Where, $\alpha$ is the angle subtended by the arc at the center of the circle and $R$ is the radius of the circle.

Now,

When we see the diagram, for the $arc(AXB)$, If we join the points $A$ and $B$ towards the center of the circle $O$ that is the radius $R$ of the circle, then, the $arc(AXB)$ will subtend an angle $\alpha _{1}$ at the center of the circle. Hence,

$arc(AXB)=R\alpha _{1}$

Similarly, for the $arc(CYD)$, lets assume the angle subtended at the center be $\alpha _{2}$. Hence, we get

$arc(CYD)=R\alpha _{2}$

We have been given that

$arc(AXB)$ ≅ $arc(CYD)$

$R\alpha _{1}$ ≅ $R\alpha _{2}$

$\alpha _{1}$ ≅ $\alpha _{2}$

If the angle subtended at the center are congruent then, the sides opposite to the congruent angles are also similar.

$AB$ ≅ $CD$

We have, the value of $AB=6cm$. Hence,

$CD$ ≅ $6cm$

Final answer:

Hence, the length of the chord will also be equal to 6 cm.

Although your question is incomplete, you might be referring to the diagram below.