# Lesson Worksheet: Tangents of a Circle Mathematics • 11th Grade

In this worksheet, we will practice using the properties of tangents of circles to find missing angles or side lengths.

Q1:

Line is tangent to a circle of center at the point . Given that and , what is ? Q2:

Determine and , rounding to the nearest hundredth. • A12.29 cm, 12.29 cm
• B12.29 cm, 10.73 cm
• C4.09 cm, 16.73 cm
• D10.73 cm, 10.73 cm

Q3:

Find the value of . Q4:

In the figure below, is the center of the circle, , , , and is a tangent. Find the perimeter of the figure . Q5:

In the figure, chord of the larger of the concentric circles is tangent to the smaller circle at . Given that the radii of the circles are 26 cm and 16.1 cm, what is the length of to the nearest tenth of a centimeter? Q6:

Given that , , and , find , rounded to the nearest hundredth. Q7:

Given that , where and are tangent to the circle at and , find . Q8:

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

Q9:

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,

Q10:

In the following figure, a circle with radius 6 is inscribed in a quadrilateral . If is the midpoint of , , and , find the area of triangle . 