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Worksheet: Tangents and Angles of Tangency

Q1:

Given that οƒͺ 𝐡 𝐢 is a tangent to the circle, find π‘š ∠ 𝐴 𝐡 𝐢 .

Q2:

Given that οƒͺ 𝐡 𝐢 is a tangent to the circle, find π‘š ∠ 𝐴 𝐡 𝐢 .

Q3:

Given that οƒͺ 𝐡 𝐢 is a tangent to the circle below, find π‘š ∠ 𝐴 𝐡 𝐢 and 𝑦 ∘ .

  • A 2 2 6 ∘ , 226
  • B 1 1 3 ∘ , 113
  • C 2 2 6 ∘ , 113
  • D 1 1 3 ∘ , 226

Q4:

Given that οƒͺ 𝐡 𝐢 is a tangent to the circle below, find π‘š ∠ 𝐴 𝐡 𝐢 and 𝑦 ∘ .

  • A 1 1 6 ∘ , 116
  • B 5 8 ∘ , 58
  • C 1 1 6 ∘ , 58
  • D 5 8 ∘ , 116

Q5:

Given that οƒͺ 𝐡 𝐢 is a tangent to the circle below, find π‘š ∠ 𝐴 𝐡 𝐢 and 𝑦 ∘ .

  • A 2 1 8 ∘ , 218
  • B 1 0 9 ∘ , 109
  • C 2 1 8 ∘ , 109
  • D 1 0 9 ∘ , 218

Q6:

is tangent to the circle at . Find .

  • A
  • B
  • C

Q7:

Given that  𝐴 𝐷 is a tangent to the circle, find π‘š ∠ 𝐡 𝐴 𝐷 .

Q8:

If , find .

  • A
  • B
  • C
  • D

Q9:

Given that  𝐴 𝐷 is a tangent to the circle and π‘š ∠ 𝐢 𝐴 𝐷 = 9 7 ∘ , find π‘š ∠ 𝐴 𝐡 𝐢 and 𝑦 .

  • A π‘š ∠ 𝐴 𝐡 𝐢 = 8 3 ∘ , 𝑦 = 8 3
  • B π‘š ∠ 𝐴 𝐡 𝐢 = 1 6 6 ∘ , 𝑦 = 1 6 6
  • C π‘š ∠ 𝐴 𝐡 𝐢 = 1 6 6 ∘ , 𝑦 = 8 3
  • D π‘š ∠ 𝐴 𝐡 𝐢 = 8 3 ∘ , 𝑦 = 1 6 6

Q10:

Given that π‘š ∠ 𝐸 𝐢 𝐷 = 5 4 ∘ and π‘š ∠ 𝐹 𝐡 𝐷 = 7 8 ∘ , find π‘₯ and 𝑦 .

  • A78, 84
  • B54, 84
  • C54, 126
  • D48, 84
  • E78, 102

Q11:

Find π‘š ∠ 𝐴 𝐢 𝐷 .

Q12:

Given that , find and .

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q13:

If and are tangents to the circle and , find .

  • A
  • B
  • C
  • D

Q14:

Find .

  • A
  • B
  • C
  • D

Q15:

Given that οƒͺ 𝐡 𝐢 is a tangent to the circle, and π‘š ∠ 𝐷 𝐴 𝐡 = 5 1 ∘ , determine π‘š ∠ 𝐴 𝐡 𝐢 and π‘š ∠ 𝐴 𝐸 𝐡 .

  • A 7 8 ∘ , 3 9 ∘
  • B 5 1 ∘ , 5 1 ∘
  • C 7 8 ∘ , 7 8 ∘
  • D 3 9 ∘ , 3 9 ∘
  • E 3 9 ∘ , 7 8 ∘

Q16:

Given that π‘š ∠ 𝐴 𝐢 𝐡 = 8 0 ∘ , find π‘š ∠ 𝐴 𝐷 𝑀 .

  • A 8 0 ∘
  • B 1 0 0 ∘
  • C 4 0 ∘
  • D 5 0 ∘

Q17:

In the figure, 𝐴 𝐡 is a diameter of circle 𝑀 . Given that π‘š ∠ 𝐢 𝐡 𝐷 = 4 3 ∘ , find π‘š ∠ 𝐴 𝑀 𝐷 .

Q18:

Find .

  • A
  • B
  • C
  • D

Q19:

Given the figure below, find and .

  • A ,
  • B ,
  • C ,
  • D ,

Q20:

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

  • A
  • B
  • C
  • D

Q21:

Given that , find .

  • A
  • B
  • C
  • D

Q22:

Given that , determine and .

  • A ,
  • B ,
  • C ,
  • D ,

Q23:

If π‘š ∠ 𝐴 𝐡 𝐢 = 8 3 ∘ and π‘š ∠ 𝑋 𝐴 𝐡 = 3 8 ∘ , find π‘š ∠ 𝐢 𝐷 𝐡 .

Q24:

Find .

  • A
  • B
  • C
  • D

Q25:

Given that βƒ–     βƒ— 𝐡 𝐢 is a tangent to the circle, and π‘š ∠ 𝐡 𝐴 𝐷 = 6 3 ∘ , find π‘š ∠ 𝐴 𝐡 𝐢 and π‘š ∠ 𝐴 𝐸 𝐡 .

  • A π‘š ∠ 𝐴 𝐡 𝐢 = 2 7 ∘ , π‘š ∠ 𝐴 𝐸 𝐡 = 5 4 ∘
  • B π‘š ∠ 𝐴 𝐡 𝐢 = 5 4 ∘ , π‘š ∠ 𝐴 𝐸 𝐡 = 5 4 ∘
  • C π‘š ∠ 𝐴 𝐡 𝐢 = 5 4 ∘ , π‘š ∠ 𝐴 𝐸 𝐡 = 2 7 ∘
  • D π‘š ∠ 𝐴 𝐡 𝐢 = 2 7 ∘ , π‘š ∠ 𝐴 𝐸 𝐡 = 2 7 ∘