Question

17. The circle in the figure below has center o_{i} which of the following measures for the figure would be ufficient by itself to determine the radius of the circle?PI. The length of arc PQRII. The perimeter of triangle OPRRIII. The length of chord PRA. NoneB. I onlyC. II onlyD. I and III

Answer 1

Two of the formulas for solving a length, involves the radius r. These formulas are the following:

$\begin{gathered} \text{Arc Length}=\theta r \\ \text{Chord Length}=2\times\sqrt{r² -d²}\text{ or }2\times r\times\sin \mleft(\frac{c}{2}\mright) \end{gathered}$

It follows that these two, by algebraic manipulation, is sufficient by itself to determine the radius of the circle.