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

Q1:

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

• A
• B
• C
• D

Q2:

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

• A
• B
• C
• D

Q3:

Given that , find .

• A
• B
• C
• D

Q4:

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 ?

• A 20, 20
• B 10, 30
• C 30, 10
• D 15, 25

Q5:

Given that is a tangent to the circle with centre 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 ?

• A
• B
• C
• D
• E

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 .

• A
• B
• C
• D

Q10:

Given that , find and .

• A ,
• B ,
• C ,
• D ,

Q11:

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

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:

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

• A 8 cm
• B 1 cm
• C 7 cm
• D 6 cm

Q14:

On which of the following does the point lie?

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

Q15:

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

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

Q16:

Where is the point in relation to the circle ?

• Aoutside
• Binside
• Con