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.