# Lesson Worksheet: Positions of Points, Straight Lines, and Circles with respect to Circles Mathematics

In this worksheet, we will practice finding the positions of points, straight lines, and circles with respect to other circles.

**Q1: **

A circle has a radius of 90 cm. A point lies on the circle at a distance of cm from the center. Which of the following is true?

- A
- B
- C

**Q2: **

A line intersects a circle with center . Point lies on and is inside the circle. If the radius of the circle is 8 cm, , and we set , in what interval does the value of belong?

- A
- B
- C
- D

**Q3: **

Consider a circle of center with a radius and a point on a line , where the line and . Which of the following is true?

- A
- B
- C

**Q4: **

Circle has radius 65. Suppose is on a line and is perpendicular to . If what can be said of how lies with respect to the circle?

- AΒ is a tangent to circle
- BΒ is a secant to circle
- CΒ is outside of circle

**Q5: **

Given that is a tangent to the circle with center and , find .

**Q6: **

In the given figure, is a tangent to a circle with center at , is a diameter, , and . Find the value of in degrees.

**Q7: **

Consider two circles and with a common tangent at point . How many elements are there in the set ?

**Q8: **

Suppose we have two circles, one with center and radius and one with center and radius . Given that the circles intersect at two distinct points, which of the following is the correct range of values for the length ?

- A
- B
- C
- D
- E

**Q9: **

Two circles with centers and are tangent at . Given that , find .

**Q10: **

Given that and , find the length of .

- A29 cm
- B cm
- C26 cm
- D832 cm