Test Questions on Perpendicular Bisector of Chords and Congruent Chords

📚 Quick Study Guide

• 📐 A perpendicular bisector of a chord is a line that is perpendicular to the chord and passes through its midpoint.
• ✨ If a line passes through the center of a circle and is perpendicular to a chord, then it bisects the chord.
• 🎯 If a line bisects a chord and passes through the center of the circle, then it is perpendicular to the chord.
• 📏 Congruent chords are chords that have the same length.
• 🔄 In the same circle or congruent circles, if two chords are congruent, then their corresponding arcs are congruent.
• 📍 In the same circle or congruent circles, if two arcs are congruent, then their corresponding chords are congruent.
• 🔑 Chords equidistant from the center of a circle are congruent. Conversely, congruent chords are equidistant from the center.

Practice Quiz

1. Question 1: If a radius of a circle is perpendicular to a chord, which of the following is true?
   1. A) It bisects the chord.
   2. B) It is parallel to the chord.
   3. C) It forms an acute angle with the chord.
   4. D) It does not intersect the chord.
2. Question 2: In circle P, chord AB is 8 cm long, and the distance from the center P to chord AB is 3 cm. What is the radius of circle P?
   1. A) 4 cm
   2. B) 5 cm
   3. C) 6 cm
   4. D) 7 cm
3. Question 3: If two chords in a circle are congruent, then which of the following must be true?
   1. A) They are parallel.
   2. B) They are perpendicular.
   3. C) Their corresponding arcs are congruent.
   4. D) They bisect each other.
4. Question 4: Chord XY is 12 units long and is 5 units from the center of circle O. Chord ZW is also 5 units from the center of circle O. What is the length of chord ZW?
   1. A) 6 units
   2. B) 10 units
   3. C) 12 units
   4. D) 24 units
5. Question 5: A chord CD is bisected by a radius OE at point F. If CD = 10 and OF = 4, what is the length of the radius OE?
   1. A) 5
   2. B) 6
   3. C) $\sqrt{41}$
   4. D) $\sqrt{29}$
6. Question 6: In circle A, chords BC and DE are congruent. If the measure of arc BC is 70 degrees, what is the measure of arc DE?
   1. A) 35 degrees
   2. B) 70 degrees
   3. C) 110 degrees
   4. D) 140 degrees
7. Question 7: Line L is the perpendicular bisector of chord MN. If MN = 16 and the radius of the circle is 10, how far is MN from the center of the circle?
   1. A) 4
   2. B) 5
   3. C) 6
   4. D) 8