# Lesson Worksheet: Common Chords to Two Circles Mathematics

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

**Q1: **

Two circles and intersect at points and , where . The point satisfies and . is a point on the circle such that is a tangent of . Also, intersects the circle at and , where and . Find the length of and to two decimal places.

- A,
- B,
- C,
- D,

**Q2: **

Find .

**Q3: **

In the figure, circles and intersect at and , and . What is ?

**Q5: **

Suppose . What is ?

**Q6: **

In the figure, circles and intersect at and . If and , determine to the nearest tenth.

**Q7: **

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.

**Q8: **

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
cm^{2} and cm^{2}.

**Q9: **

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

**Q10: **

Given two different circles that both pass through the points and , which line contains the centers of both circles?

- AThe perpendicular bisector of
- B
- CA line perpendicular to that does not bisect it
- DA line parallel to