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What is the measure of ZBDC?What is the measure of arc length BC?

What Is The Measure Of ZBDCWhat Is The Measure Of Arc Length BC class=

Sagot :

SOLUTION

Step 1:

To find the measure of

Step 2:

The angle subtended by an arc at the centre is twice the angle subtended at the circumference. More simply, the angle at the centre is double the angle at the circumference.

Step 3:

Dividing both sides by 2, we have;

[tex]\begin{gathered} <\text{BDC = }\frac{BOC}{2}\text{ = }\frac{138}{2} \\ \\

Step 4:

We are to find the measure of arc length BC;

Angle BOC is given as 138

[tex]\begin{gathered} \frac{\theta}{360}\text{ x 2 }\pi\text{ r} \\ \\ \frac{138}{360}\text{ x 2 x 3.14 x r } \\ \\ 2.407r \end{gathered}[/tex]

Note: Since the value of the radius was not given so we need to express our answer in term of r.

The measure of arc length BC is 2.407r, where r is the radius.

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