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# 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: **

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

**Q2: **

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

**Q3: **

Given that is a tangent to the circle at the point , , and the point is the midpoint of , find the value of .

**Q4: **

The circumference of a circle with center is 259 and is tangent at . Calculate the length of to the nearest hundredth.

**Q5: **

In the figure, two circles with centres and touch externally at which is a point on the common tangent , where is a common tangent. Suppose and . Find to the nearest tenth.

**Q6: **

On which of the following does the point lie?

- Athe circleΒ
- BtheΒ
- Cthe straight lineΒ
- DtheΒ

**Q7: **

Draw a triangle in which , , and , and then draw a circle whose center is and radius is 5 cm. Determine whether point is located on, inside, or outside the circle.

- AInside the circle
- BOn the circle
- COutside the circle

**Q8: **

The radii of the two circles on the common center are 3 cm and 4 cm. What is the length of ?

**Q9: **

Circles and have radii of
29 cm and
18 cm and touch internally at
. Given that is a common tangent to
the circles and that has an area of
55 cm^{2}, what is the length
of ?

**Q10: **

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