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Theorems Related to Chords of a Circle Video Lecture | Mathematics (Maths) Class 9
FAQs on Theorems Related to Chords of a Circle Video Lecture - Mathematics (Maths) Class 9
| 1. What are the properties of a chord in a circle? |  |
Ans. A chord in a circle is a line segment that joins two points on the circumference of the circle. The properties of a chord are:
- The perpendicular bisector of a chord passes through the center of the circle.
- The chords that are equidistant from the center of the circle are equal in length.
- The longest chord in a circle is the diameter, which passes through the center of the circle.
| 2. How can we find the length of a chord in a circle? | |
Ans. To find the length of a chord in a circle, we can use the following formula:
Length of the chord = 2 * √(r^2 - d^2)
where r is the radius of the circle and d is the perpendicular distance between the chord and the center of the circle.
| 3. What is the relationship between the angle subtended by a chord and its corresponding arc? | |
Ans. The angle subtended by a chord at the center of a circle is double the angle subtended by the same chord at any point on the circumference of the circle. In other words, if an arc is formed by a chord, the angle subtended by the chord at the center of the circle is twice the angle subtended by the same chord at any point on the circumference.
| 4. Can a circle have more than one chord with the same length? | |
Ans. Yes, a circle can have more than one chord with the same length. In fact, if two chords are equidistant from the center of the circle, they will be of equal length. Additionally, if a chord is perpendicular to the diameter of a circle, it will be the shortest possible chord and any other chord parallel to it will have the same length.
| 5. What is the significance of the perpendicular bisector of a chord in a circle? | |
Ans. The perpendicular bisector of a chord in a circle passes through the center of the circle. This property is significant because it allows us to find the center of the circle when the endpoints of the chord are known. It also helps in constructing and identifying congruent chords in a circle.
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