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

Find The Measure Of CD MCD Degrees class=

Sagot :

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,

[tex]OC=7[/tex]            (Given)

[tex]OC=OD=7[/tex]          (Radii of same circle)

[tex]CD=7[/tex]            (Given)

Since [tex]OC=CD=OD[/tex] all sides are equal, therefore, the triangle OCD is an equilateral triangle.

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

[tex]m\angle COD=60^\circ[/tex]

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

[tex]m(arcCD)=m\angle COD[/tex]

[tex]m(arcCD)=60^\circ[/tex]

Therefore, the measure of arc CD is 60 degrees.

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