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# Worksheet: Finding the Measures of Segments That Intersect in the Exterior of a Circle

Q1:

If , , , find the length of .

Q2:

If , , , find the length of .

Q3:

If , , and , find the lengths of and .

• A ,
• B ,
• C ,
• D ,
• E ,

Q4:

If , , and , find the lengths of and .

• A ,
• B ,
• C ,
• D ,
• E ,

Q5:

Given , and , find the length of rounded to the nearest hundredth.

Q6:

Given , and , find the length of rounded to the nearest hundredth.

Q7:

Find length to the nearest integer.

Q8:

In the figure shown, the circle has a radius of 12 cm, , and . Determine the distance from to the center of the circle, , and the length of , rounding your answers to the nearest tenth.

• A 19.6 cm, 20.2 cm
• B 11.5 cm, 20.2 cm
• C 3.4 cm, 26.6 cm
• D 3.4 cm, 20.5 cm

Q9:

Determine the value of in the given figure, assuming the segment that appears to be tangent is a tangent.

Q10:

Given that is tangent to the circle and that and lie on the circle, determine the value of to the nearest tenth.

Q11:

In the figure, , , , and . Mason and Chloe were trying to find the value of . Mason wrote , and Chloe wrote . Who is correct?

• AChloe
• BMason

Q12:

Given that the middle line segment is a tangent to both circles, find .

Q13:

In the shown figure, is tangent to the circle, , , and . Determine the lengths of and .

• A ,
• B ,
• C ,
• D ,

Q14:

Given that , , , and , find the lengths of and .

• A ,
• B ,
• C ,
• D ,
• E ,

Q15:

If , , , and , find the lengths of and .

• A ,
• B ,
• C ,
• D ,