Worksheet: Applications of Intersecting Chords and Secants

In this worksheet, we will practice finding the length of a part of a chord or a secant that intersects with another chord or secant, inside or outside a circle.

Q1:

If 𝐸 𝐶 = 1 0 c m , 𝐸 𝐷 = 6 c m , 𝐸 𝐵 = 5 c m , find the length of 𝐸 𝐴 .

Q2:

If 𝐸 𝐴 𝐸 𝐵 = 5 3 , 𝐸 𝐶 = 1 2 c m , and 𝐸 𝐷 = 5 c m , find the lengths of 𝐸 𝐵 and 𝐵 𝐴 .

  • A 𝐸 𝐵 = 4 c m , 𝐵 𝐴 = 6 c m
  • B 𝐸 𝐵 = 6 c m , 𝐵 𝐴 = 1 0 c m
  • C 𝐸 𝐵 = 1 0 c m , 𝐵 𝐴 = 6 c m
  • D 𝐸 𝐵 = 6 c m , 𝐵 𝐴 = 4 c m
  • E 𝐸 𝐵 = 2 4 c m , 𝐵 𝐴 = 2 0 c m

Q3:

In the figure shown, the circle has a radius of 12 cm, 𝐴 𝐵 = 1 2 c m , and 𝐴 𝐶 = 3 5 c m . Determine the distance from 𝐵 𝐶 to the centre of the circle, 𝑀 , and the length of 𝐴 𝐷 , rounding your answers to the nearest tenth.

  • A 19.6 cm, 20.2 cm
  • B 11.5 cm, 20.2 cm
  • C 3.4 cm, 26.6 cm
  • D 3.4 cm, 20.5 cm

Q4:

Given that 𝐸 𝐴 = 1 1 𝑥 , 𝐸 𝐵 = 2 1 𝑥 , 𝐸 𝐶 = 2 2 , and 𝐸 𝐷 = 4 2 , find the value of 𝑥 .

  • A 𝑥 = 1 . 0 5
  • B 𝑥 = 4 6 . 2
  • C 𝑥 = 0 . 5 5
  • D 𝑥 = 2

Q5:

Are the points 𝐴 , 𝐵 , 𝐶 , and 𝐷 lying on a circle?

  • Ayes
  • Bno

Q6:

Given that the points 𝐴 , 𝐵 , 𝐶 , and 𝐷 lie on a circle, find the length of 𝐵 𝐴 .

Q7:

In the figure below, 𝐵 𝐶 is a diameter of the circle 𝑀 , 𝐴 𝐵 = 𝐴 𝐶 , 𝑚 𝐵 𝐴 𝐶 = 6 0 , 𝐵 𝑋 = 2 2 . 9 c m , and 𝑀 𝑋 𝐴 𝐵 . Find the length of 𝐴 𝐸 .

Q8:

A circle has centre 𝑀 and radius 13 cm. A line passes through the points 𝐵 , 𝐶 , and 𝐷 where 𝐶 and 𝐷 are on the circle, 𝐵 is 25 cm from the point 𝑀 , and 𝐶 𝐵 = 𝐶 𝐷 . Calculate the length of 𝐶 𝐷 and the perpendicular distance 𝑥 between the line and the point 𝑀 . Round your answers to 2 decimal places.

  • A 𝐶 𝐷 = 1 1 4 . 0 0 c m , 𝑥 = 1 1 3 . 2 6 c m
  • B 𝐶 𝐷 = 2 . 4 5 c m , 𝑥 = 1 2 . 9 4 c m
  • C 𝐶 𝐷 = 7 . 5 5 c m , 𝑥 = 1 3 . 0 0 c m
  • D 𝐶 𝐷 = 1 5 . 1 0 c m , 𝑥 = 1 0 . 5 8 c m

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