# Lesson Worksheet: Perpendicular Bisector of a Chord Mathematics

In this worksheet, we will practice using the theory of the perpendicular bisector of a chord from the center of a circle and its converse to solve problems.

Question 2

The radius of the circle below is 87 cm, , and is the midpoint of . Given that intersects at and , find the length of .

Question 5

In circle , suppose and . Find the lengths of and to the nearest hundredth.

- A5.71, 11.00
- B11.43, 1.60
- C22.00, 1.60
- D11.43, 11.00

Question 6

In the given circle, cm and cm. Determine the lengths of and .

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

Question 7

The distance between the two lines and is 13 and . If the radius of the circle is 10.5, what is the length of ? Round your answer to two decimal places.

Question 8

Given that , and cm, determine the length of .

Question 9

Given that , , , and , determine the value of and the length of .

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

Question 10

In the circle , if , find the length of .

Question 11

In circle , . Find .

Question 12

The radius of circle is 60.9 cm, and . What is the area of ?

Question 13

In the figure, the two circles are concentric at and . Calculate the area of the shaded region, to the nearest hundredth.

Question 14

The circumference of circle is 36.6 cm. Calculate to the nearest tenth.

Question 15

In the figure, the smaller of the concentric circles is tangent to chord at . If the large circle has radius 67 cm, and , what is the radius of the smaller circle?

Question 16

Point is at a distance 13 from , which is the center of a circle of radius 7.3. Draw ray to intersect the circle at and , with between and . If , what is ?

Question 17

Given that and are the centers of two circles which intersect at and where , , and , find the length of . Round the answer to the nearest hundredth.

Question 18

A circle has a radius of 48.9 cm. The point lies 48.3 cm from its center. If a chord satisfies and , what is its length?

Question 19

The radii of two concentric circles are 55 cm and 40 cm. is a chord in the larger circle, and intersects the smaller circle first at and then at . Given that , find the length of to the nearest hundredth.

Question 21

Which of the choices below can be a chord length in a circle whose diameter is 19 cm?

- A21 cm
- B23 cm
- C38 cm
- D10 cm

Question 22

A circle with center has a radius of 22 cm. The point lies 19 cm from and belongs to the chord . Given that , calculate the perpendicular distance between and the chord, giving your answer to the nearest whole number.

Question 23

A circle of center has a radius of 13 and a point is at a distance of 20 from its center. A line that is a tangent to the circle at a point is drawn through . Calculate the length of . Round your answer to the nearest whole number.

Question 25

Using the figure and the fact that , determine the diameter of the circle.