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

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:

In the given figure, is tangent to the circle with center . If the length of is 3, the length of is 5, and the length of is 40, what are the lengths of and ?

• A30, 10
• B20, 20
• C15, 25
• D10, 30

Q3:

The radii of the two circles on the common center are 3 cm and 4 cm. What is the length of ? Q4:

Given that , find . Q5:

Given that is a tangent to the circle with center and , find . Q6:

Identify all the radii of circle . • A
• B
• C

Q7:

If is a tangent to the circle at the point , and , what is ? Q8:

Given that is a tangent to the circle at the point , , and the point is the midpoint of , find the value of . Q9:

Given that is a tangent to the circle and , calculate . Q10:

The circumference of a circle with center is 259 and is tangent at . Calculate the length of to the nearest hundredth. Q11:

Given that , find and . • A,
• B,
• C,
• D,

Q12:

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. Q13:

Describe the position of the straight line with respect to the circle .

• AThe straight line is a secant to the circle.
• BThe straight line is outside the circle.
• CThe straight line is a tangent to the circle.

Q14:

Where is the point in relation to the circle ?

• Aon
• Binside
• Coutside

Q15:

On which of the following does the point lie?

• Athe circle
• Bthe-axis
• Cthe straight line
• Dthe-axis

Q16:

In the given figure, is a tangent to a circle with center at , is a diameter, , and . Find the value of in degrees. Q17:

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