Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Start Practicing

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

Q1:

In the figure below, is a tangent to the circle at , is a diameter, , and . Find the value of in degrees.

  • A
  • B
  • C
  • D

Q2:

In the figure below, is a tangent to the circle at , is a diameter, , and . Find the value of in degrees.

  • A
  • B
  • C
  • D

Q3:

Given that , find .

  • A
  • B
  • C
  • D

Q4:

In the given figure, 𝑃 𝑄 is tangent to the circle with center 𝐵 .

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

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

Q5:

Given that 𝐵 𝐶 is a tangent to the circle with centre 𝑀 and 𝐴 𝑀 𝐷 = 9 7 , find 𝐶 𝐵 𝐷 .

Q6:

Identify all the radii of circle .

  • A
  • B
  • C

Q7:

If 𝐸 𝐷 is a tangent to the circle at the point 𝐵 , and 𝑚 𝐸 𝐵 𝐶 = 4 0 , what is 𝑚 𝐴 𝐶 𝐵 ?

  • A 6 5
  • B 4 0
  • C 3 7 . 5
  • D 7 5
  • E 5 2 . 5

Q8:

Given that 𝐴 𝐵 is a tangent to the circle 𝑀 at the point 𝐵 , 𝑚 𝐵 𝑀 𝐶 = 3 𝑚 𝐴 , and the point 𝐶 is the midpoint of 𝐷 𝐸 , find the value of 𝑥 .

Q9:

Given that is a tangent to the circle and , calculate .

  • A
  • B
  • C
  • D

Q10:

Given that , find and .

  • A ,
  • B ,
  • C ,
  • D ,

Q11:

The circumference of circle 𝑀 is 259 and 𝑍 𝑌 is tangent at 𝑌 . Calculate the length of 𝑍 𝑌 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 𝐿 , where 𝐴 𝐵 is a common tangent. Suppose 𝐴 𝐵 = 𝑀 𝑁 = 4 5 . 5 c m and 𝐵 𝐶 = 3 0 . 5 c m . Find 𝐴 𝑁 to the nearest tenth.

Q13:

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

  • A 8 cm
  • B 1 cm
  • C 7 cm
  • D 6 cm

Q14:

On which of the following does the point lie?

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

Q15:

Describe the position of the straight line 𝐿 5 𝑥 + 4 𝑦 1 = 0 with respect to the circle 𝑥 + 𝑦 + 6 𝑥 8 𝑦 + 9 = 0 2 2 .

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

Q16:

Where is the point ( 4 , 2 ) in relation to the circle ( 𝑥 4 ) + ( 𝑦 1 ) = 1 2 2 ?

  • Aoutside
  • Binside
  • Con