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.


Line 𝐴𝐶 is tangent to a circle of center 𝑀 at the point 𝐴. Given that 𝐵𝑀=55cm and 𝐴𝐶=96cm, what is 𝐵𝐶?


Determine 𝐴𝑀 and 𝐴𝐵, 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


Find the value of 𝑥.


In the figure below, 𝑀 is the center of the circle, 𝑀𝐵=15cm, 𝐴𝐵=20cm, 𝑀𝐶=9cm, and 𝐴𝐵 is a tangent. Find the perimeter of the figure 𝐴𝐵𝐶𝑀.


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


Given that 𝐵𝑁=11cm, 𝐴𝑀=21cm, and 𝑁𝑀=55cm, find 𝐴𝐵, rounded to the nearest hundredth.


Given that 𝑚𝑀𝐶𝐵=49, where 𝐴𝐵 and 𝐴𝐶 are tangent to the circle at 𝐵 and 𝐶, find 𝑚𝐵𝐴𝑀.


Given that 𝑚𝑀𝐴𝐶=36, determine 𝑚𝐵𝐴𝑀 and 𝑚𝐴𝑀𝐶.

  • A36, 54
  • B54, 54
  • C54, 36
  • D36, 36


The two circles 𝑀 and 𝑁 are touching externally. 𝐹𝐴 is a common tangent to them at 𝐴 and 𝐵 respectively, 𝐹𝐶 is a common tangent to them at 𝐶 and 𝐷 respectively. Given that 𝐴𝐵=11.01cm, and 𝐶𝐷=(𝑦5)cm, find 𝑥 and 𝑦.

  • A𝑥=12.31, 𝑦=11.01
  • B𝑥=11.01, 𝑦=12.31
  • C𝑥=14.31, 𝑦=16.01
  • D𝑥=13.01, 𝑦=17.31


In the following figure, a circle with radius 6 is inscribed in a quadrilateral 𝐴𝐵𝐶𝐷. If 𝐸 is the midpoint of 𝐴𝐵, 𝐴𝐵=10cm, and 𝐶𝐺=6cm, find the area of triangle 𝐵𝐶𝑀.

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