Question

Find the measure of CD. mCD= [?] degrees

Answer 1

Given:

A circle with radius 7 units and chord CD = 7 units.

To find:

The measure of arc CD.

Solution:

Let O be the center of the circle.

In triangle OCD,

$OC=7$            (Given)

$OC=OD=7$          (Radii of same circle)

$CD=7$            (Given)

Since $OC=CD=OD$ all sides are equal, therefore, the triangle OCD is an equilateral triangle.

Measure of each angle of an equilateral triangle is 60 degrees. So,

$m\angle COD=60^\circ$

The measure of central angle is equal to the measure of corresponding arc.

$m(arcCD)=m\angle COD$

$m(arcCD)=60^\circ$

Therefore, the measure of arc CD is 60 degrees.