Worksheet: Common Chords to Two Circles

In this worksheet, we will practice using the properties of the common chord between two intersecting circles to solve problems.

Q1:

Two circles 𝑀 and 𝑁 intersect at points 𝐴 and 𝐵, where 𝐵𝐴=15cm. The point 𝐶 satisfies 𝐶𝐵𝐴 and 𝐶𝐵𝐴. 𝐹 is a point on the circle 𝑁 such that 𝐶𝐹 is a tangent of 𝑁. Also, 𝐶𝐸 intersects the circle 𝑀 at 𝐷 and 𝐸, where 𝐶𝐷=8cm and 𝐷𝐸=5cm. Find the length of 𝐶𝐴 and 𝐶𝐹 to two decimal places.

  • A𝐶𝐴=2.31cm, 𝐶𝐹=52.00cm
  • B𝐶𝐴=5.16cm, 𝐶𝐹=10.20cm
  • C𝐶𝐴=20.16cm, 𝐶𝐹=10.20cm
  • D𝐶𝐴=44.64cm, 𝐶𝐹=52.00cm

Q2:

Given that 𝐵𝐶=41.7cm and 𝑀𝐷=60cm, find the length of 𝐴𝐷 to the nearest tenth.

Q3:

Find 𝑚𝐵𝐴𝐷.

Q4:

In the figure, circles 𝑀 and 𝑁 intersect at 𝐴 and 𝐵, and 𝑚𝐸=48.3. What is 𝑚𝑍𝑁𝑋?

Q5:

Two congruent circles of radius 𝑟 cm intersect. Their centers are 56 cm apart, and their common chord has a length of 42 cm. Determine 𝑟.

Q6:

Suppose 𝐴𝑀=49cm. What is 𝐴𝐵?

Q7:

In the figure, circles 𝑀 and 𝑁 intersect at 𝐴 and 𝐵. If 𝐺𝐶=𝐶𝐸 and 𝑚𝐶𝑀𝑁=(6𝑥6), determine 𝑥 to the nearest tenth.

Q8:

Two circles of radii 8 cm and 17 cm intersect at two points, and the distance between their centers is 15 cm. Find the length of the common chord.

Q9:

Find the length of the common chord of two intersecting circles if the distance between the centers of the two circles is 25 cm and the areas of the circles are 400𝜋 cm2 and 225𝜋 cm2.

Q10:

If the common chord of two intersecting circles is 24 cm and the circumferences of the circles are 40𝜋 cm and 30𝜋 cm, find the distance between the centers of the two circles.

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