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Worksheet: Applications of Intersecting Chords and Secants

Q1:

A circle has center 𝑀 and radius 13 cm. A line passes through the points 𝐡 , 𝐢 , and 𝐷 where 𝐢 and 𝐷 are on the circle, 𝐡 is 25 cm from the point 𝑀 , and 𝐢 𝐡 = 𝐢 𝐷 . Calculate the length of 𝐢 𝐷 and the perpendicular distance π‘₯ between the line and the point 𝑀 . If necessary, round your answers to 2 decimal places.

  • A 𝐢 𝐷 = 1 1 4 . 0 0 c m , π‘₯ = 1 1 3 . 2 6 c m
  • B 𝐢 𝐷 = 2 . 4 5 c m , π‘₯ = 1 2 . 9 4 c m
  • C 𝐢 𝐷 = 7 . 5 5 c m , π‘₯ = 1 3 . 0 0 c m
  • D 𝐢 𝐷 = 1 5 . 1 0 c m , π‘₯ = 1 0 . 5 8 c m

Q2:

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

Q3:

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

Q4:

In the figure below, 𝐡 𝐢 is a diameter of the circle 𝑀 , 𝐴 𝐡 = 𝐴 𝐢 , π‘š ∠ 𝐡 𝐴 𝐢 = 6 0 ∘ , 𝐡 𝑋 = 2 2 . 9 c m , and 𝑀 𝑋 βŸ‚ 𝐴 𝐡 . Find the length of 𝐴 𝐸 .

Q5:

Are the points 𝐴 , 𝐡 , 𝐢 , and 𝐷 lying on a circle?

  • Ayes
  • Bno

Q6:

Are the points 𝐴 , 𝐡 , 𝐢 , and 𝐷 lying on a circle?

  • Ayes
  • Bno

Q7:

Given that 𝐸 𝐴 = 1 1 π‘₯ , 𝐸 𝐡 = 2 1 π‘₯ , 𝐸 𝐢 = 2 2 , and 𝐸 𝐷 = 4 2 , find the value of π‘₯ .

  • A π‘₯ = 1 . 0 5
  • B π‘₯ = 4 6 . 2
  • C π‘₯ = 0 . 5 5
  • D π‘₯ = 2

Q8:

Given that 𝐸 𝐴 = 1 2 π‘₯ , 𝐸 𝐡 = 7 π‘₯ , 𝐸 𝐢 = 2 7 , and 𝐸 𝐷 = 2 8 , find the value of π‘₯ .

  • A π‘₯ = 5 . 3 3
  • B π‘₯ = 2 5 . 2
  • C π‘₯ = 2 . 8 9
  • D π‘₯ = 3
  • E π‘₯ = 4 . 9 6