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# Circles

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# The Basics of Circles Exercises

### Example 1

Consider a circle with center *O* and radius 20 m. Is *P* such that *OP* = 8 m in the interior of the circle, in the exterior of the circle, or on the circle?

### Example 2

Consider a circle with center *O* and radius 20 m. Is *Q* such that *OQ* = 30 cm in the interior of the circle, in the exterior of the circle, or on the circle?

### Example 3

Consider a circle with center *O* and radius 20 m. Is *S* such that *OS* = 20 m in the interior of the circle, in the exterior of the circle, or on the circle?

### Example 4

Consider a circle with center *O* and radius 20 m. Is *O* in the interior of the circle, in the exterior of the circle, or on the circle?

### Example 5

Consider a circle with center *O* and radius 20 m. Is *T* such that *OT* = 100 m in the interior of the circle, in the exterior of the circle, or on the circle?

### Example 6

Consider a circle with center *O* and radius 20 m. Is *U* such that *OU* > *OS* in the interior of the circle, in the exterior of the circle, or on the circle?

### Example 7

Consider a circle with center *O* and radius 20 m. Is *V* such that *OS* < *OV* < *OU* in the interior of the circle, in the exterior of the circle, or on the circle?

### Example 8

In the figure below, points *A*, *B*, *C*, and *D* are on ⊙*O*. m∠*BOC* = 50°, m∠*COD* = 140°, m∠*DOA* = 65°. What is m∠*AOB*?

### Example 9

In the figure below, suppose now that m∠*BOC* = 67° instead of 50°. How does the measure of m∠*AOB* change?