# 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.

Q1:

In the figure, circles and are congruent, , , and . Find the length of . 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 . Q4:

is a chord in circle whose radius is 25.5 cm. If , what is the length of ? Q5:

Given and , find . 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.