Lesson Worksheet: Tangents of a Circle Mathematics

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

Q1:

Given that ⃖⃗𝐴𝐵 is a tangent to the circle 𝑀 at 𝐴, and 𝑚∠𝑀𝐵𝐸=151∘, find 𝑚∠𝐴𝑀𝐵.

Q2:

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

  • Atangent
  • Bsegment
  • Cchord
  • Darc
  • Eradius

Q3:

A circle of center 𝑀 has a radius of 11 cm. If 𝐶𝐴=16.3cm, what is 𝐴𝐵? Give your answer to the nearest tenth.

Q4:

Given that 𝐴𝐶=(2𝑥−3)cm, find 𝑥 and 𝑦 to the nearest thousandth.

  • A𝑥=1.500, 𝑦=5.000
  • B𝑥=19.000, 𝑦=19.000
  • C𝑥=24.000, 𝑦=11.000
  • D𝑥=11.000, 𝑦=24.000

Q5:

Given that ⃖⃗𝐴𝐵 is a tangent to the circle 𝑀, and 𝑚∠𝑀𝐵𝐹=123∘, determine 𝑚∠𝐴𝑀𝐵.

Q6:

Given that 𝐴𝐵 is tangent to the circle 𝑀 at 𝐴, 𝐴𝑀=8.6cm, and 𝑀𝐵=12.3cm, find the length of 𝐴𝐵, and round the result to the nearest tenth.

Q7:

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

Q8:

Given that 𝐵𝐶 is a tangent to the circle and 𝑚∠𝐴𝑀𝐵=86∘, find 𝑚∠𝐴𝐵𝐶.

Q9:

Given that ⃖⃗𝐴𝐵 is a tangent to a circle with center 𝑀 and 𝑚∠𝐴𝐵𝑀=49∘, determine 𝑚∠𝐴𝐷𝐵.

Q10:

Given that 𝐴𝐵 is a tangent to the circle 𝑀 at 𝐴, 𝑚∠𝑀=130.2∘, and 𝐸 is the midpoint of 𝐶𝐷, find 𝑚∠𝐵.

Q11:

Given that 𝐴𝐵=8.2cm, find the length of 𝐵𝐶 rounding the result to the nearest hundredth.

Q12:

Given that ⃖⃗𝐴𝐵 is a tangent to the circle 𝑀 at 𝐷, 𝐴𝐶=𝐵𝐶, 𝑚∠𝐴=60∘, and 𝐴𝐷=34.7cm, determine the perimeter of △𝐴𝐵𝐶.

Q13:

Given that ⃖⃗𝐴𝐵 is a tangent to the circle of center 𝑀, find the perimeter of △𝐴𝐵𝐶.

Q14:

Suppose that, in the figure, 𝐴𝐵 is tangent to the circle at 𝐵, 𝑀𝐵=17.6cm, and 𝐴𝐶=32.4cm. What is the length of 𝐴𝐵?

Q15:

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

Q16:

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

  • AYes
  • BNo

Q17:

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

Q18:

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

  • AYes
  • BNo

Q19:

Given that 𝐴𝐵 and 𝐴𝐶 are two tangent segments to a circle at the points 𝐵 and 𝐶, and 𝐴𝐵=91cm, determine the length of 𝐴𝐶.

Q20:

Find the value of 𝑥.

Q21:

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

Q22:

Given that ⃖⃗𝐴𝐵 is a tangent to the circle 𝑀, find the length of 𝐷𝐵.

Q23:

In the figure, ⃖⃗𝑋𝑌 is tangent to circle 𝑀 at 𝑋, 𝑀𝑌 meets the circle at 𝑍, 𝑋𝑌=21cm, and 𝑌𝑍=11cm. Find the circle’s diameter to the nearest tenth.

Q24:

Line ⃖⃗𝐴𝐶 is tangent to circle 𝑀 at 𝐴. Given that 𝐵𝑀=55cm, 𝐴𝐶=96cm, what is 𝐵𝐶?

Q25:

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=(𝑦−5)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

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