# Worksheet: Perpendicular Bisector of a Chord

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.

**Q2: **

Points and are midpoints of segments and respectively. If , what is ?

**Q3: **

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

**Q6: **

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

**Q7: **

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

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

**Q8: **

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.

**Q9: **

Given that , and cm, determine the length of .

**Q10: **

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

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

**Q11: **

Given that , , and , find the length of .

**Q12: **

In the circle , if , find the length of .

**Q13: **

In circle , . Find .

**Q14: **

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

**Q15: **

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

**Q16: **

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

**Q17: **

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?

**Q18: **

If , find the range of values of that satisfies the data represented.

- A
- B
- C
- D

**Q19: **

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 ?

**Q20: **

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.

**Q21: **

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?

**Q22: **

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.

**Q23: **

and are two chords in the circle in two opposite sides of its center, where . If and are the midpoints of and respectively, find .

**Q24: **

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

**Q25: **

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.