Worksheet: Properties of Tangents

Q1:

Circle has radius 11 cm. If , what is ? Answer to the nearest tenth.

Q2:

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

• A
• B
• C
• D

Q3:

Find the value of .

Q4:

In the following figure, the line that appears to be tangent is tangent. Find , and then find to the nearest tenth.

• A ,
• B ,
• C ,
• D ,
• E ,

Q5:

What is the name of a line that meets a circle in exactly one point?

• Bchord
• Carc
• Dtangent
• Esegment

Q6:

In the figure, the circle has radius 5 cm. Given that is tangent at , , and , determine the length of .

• A cm
• B 16 cm
• C cm
• D 4 cm

Q7:

A circle with center has a radius of 20 cm, and is tangent to the circle at . A point lies on both the circle and the line segment . If , find .

Q8:

Given that and are two tangents, find the length of .

Q9:

Given that , find and to the nearest thousandth.

• A ,
• B ,
• C ,
• D ,

Q10:

Given that and are two tangent segments to a circle at the points and , and , determine the length of .

Q11:

and are tangents to circle at and . If the radius of the circle is 6 cm and , find the lengths of and .

• A = cm, = 12 cm
• B = cm, = cm
• C = cm, = cm
• D = 12 cm, = cm

Q12:

The two circles and are touching externally. is a common tangent to them at and respectively, is a common tangent to them at and respectively. Given that , and , find and .

• A ,
• B ,
• C ,
• D ,

Q13:

Given that , determine the lengths of and .

• A ,
• B ,
• C ,
• D ,

Q14:

In the figure, is tangent to circle at , , , and . Find to the nearest tenth.

Q15:

Lines and are tangents to circle . If , what is ?

• A
• B
• C
• D

Q16:

Find the length of .

Q17:

Given that and are two tangents to the circle at the points and , respectively, determine .

• A
• B
• C
• D

Q18:

In the figure, is tangent to circle at , meets the circle at , , and . Find the circleβs diameter to the nearest tenth.

Q19:

If I draw two tangent segments from a point outside the circle, are they equal in length?

• Ayes
• Bno

Q20:

If I draw two tangents to a circle, one from each end of a diameter, are the tangents parallel?

• Ayes
• Bno

Q21:

Line is tangent to circle at . Given that , , what is ?

Q22:

Line is tangent to circle at . Given that , , what is ?

Q23:

In the figure, line is tangent to the circle at . What is the length ?

Q24:

If two circle intersect at two points, how many common tangents do they have?

Q25:

If two circles lie outside each other, how many common tangents do they have?