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Lesson: Positions of Points, Straight Lines, and Circles with respect to Circles

Sample Question Videos

Worksheet • 16 Questions • 1 Video

Q1:

In the figure below,  𝐴 𝐡 is a tangent to the circle 𝑀 at 𝐡 , 𝐢 𝐷 is a diameter, π‘š ∠ 𝐡 𝐴 𝑀 = π‘₯ , and π‘š ∠ 𝑀 𝐷 𝐡 = 2 π‘₯ βˆ’ 5 5 . Find the value of π‘₯ in degrees.

Q2:

In the figure below,  𝐴 𝐡 is a tangent to the circle 𝑀 at 𝐡 , 𝐢 𝐷 is a diameter, π‘š ∠ 𝐡 𝐴 𝑀 = π‘₯ , and π‘š ∠ 𝑀 𝐷 𝐡 = 2 π‘₯ βˆ’ 5 . Find the value of π‘₯ in degrees.

Q3:

Given that π‘š ∠ 𝑍 π‘Œ 𝐿 = 1 2 2 ∘ , find π‘š ∠ 𝑋 .

Q4:

In the given figure, βƒ–     βƒ— 𝑃 𝑄 is tangent to the circle with centre 𝐡 .

If the length of 𝐴 𝑄 is 3, the length of 𝐡 𝑃 is 5, and the length of 𝐴 𝐡 is 40, what are the lengths of 𝐴 𝑂 and 𝑂 𝐡 ?

  • A 15, 25
  • B 10, 30
  • C 30, 10
  • D 20, 20

Q5:

Given that βƒ–     βƒ— 𝐡 𝐢 is a tangent to the circle with centre 𝑀 and ∠ 𝐴 𝑀 𝐷 = 9 7 ∘ , find ∠ 𝐢 𝐡 𝐷 .

Q6:

Identify all the radii of circle .

  • A
  • B
  • C

Q7:

If βƒ–     βƒ— 𝐸 𝐷 is a tangent to the circle at the point 𝐡 , and π‘š ∠ 𝐸 𝐡 𝐢 = 4 0 ∘ , what is π‘š ∠ 𝐴 𝐢 𝐡 ?

Q8:

Given that 𝐴 𝐡 is a tangent to the circle 𝑀 at the point 𝐡 , π‘š ∠ 𝐡 𝑀 𝐢 = 3 π‘š ∠ 𝐴 , and the point 𝐢 is the midpoint of 𝐷 𝐸 , find the value of π‘₯ .

Q9:

Given that  𝐴 𝐷 is a tangent to the circle and π‘š ∠ 𝐷 𝐴 𝐢 = 9 0 ∘ , calculate π‘š ∠ 𝐴 𝐢 𝐡 .

Q10:

Given that π‘š ∠ 𝐢 𝐷 𝐸 = 8 9 ∘ , find π‘š ∠ 𝐷 𝐡 𝐢 and π‘š ∠ 𝐴 𝐷 𝐡 .

  • A 8 9 ∘ , 5 1 ∘
  • B 5 1 ∘ , 8 9 ∘
  • C 7 6 ∘ , 3 8 ∘
  • D 7 6 ∘ , 5 1 ∘

Q11:

The circumference of circle 𝑀 is 259 and  𝑍 π‘Œ is tangent at π‘Œ . Calculate the length of 𝑍 π‘Œ to the nearest hundredth.

Q12:

In the figure, two circles with centres 𝑀 and 𝑁 touch externally at 𝐴 which is a point on the common tangent βƒ– βƒ— 𝐿 , where 𝐴 𝐡 is a common tangent. Suppose 𝐴 𝐡 = 𝑀 𝑁 = 4 5 . 5 c m and 𝐡 𝐢 = 3 0 . 5 c m . Find 𝐴 𝑁 to the nearest tenth.

Q13:

The radii of the two circles on the common centre 𝑀 are 3 cm and 4 cm. What is the length of 𝐴 𝐡 ?

Q14:

On which of the following does the point lie?

  • Athe straight line
  • Bthe -axis
  • Cthe circle
  • Dthe -axis

Q15:

Describe the position of the straight line 𝐿 ∢ 5 π‘₯ + 4 𝑦 βˆ’ 1 = 0 with respect to the circle π‘₯ + 𝑦 + 6 π‘₯ βˆ’ 8 𝑦 + 9 = 0 2 2 .

  • AThe straight line is outside the circle.
  • BThe straight line is a secant to the circle.
  • CThe straight line is a tangent to the circle.

Q16:

Where is the point ( 4 , 2 ) in relation to the circle ( π‘₯ βˆ’ 4 ) + ( 𝑦 βˆ’ 1 ) = 1 2 2 ?

  • Ainside
  • Bon
  • Coutside
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