How many equal chords are there in a circle?

There are infinite points on a circle. Therefore, we can draw infinite number of chords of given length. Hence, a circle has infinite number of equal chords.

Are two chords equal in a circle?

2) Equal-chords of congruent circles are equidistant from the corresponding centers. If two circles are congruent and AB = CD then OL = PM.



Equal Chords of a Circle.

Does a circle has finite number of equal chords?

(ii) A circle has only finite number of equal chords. (iii) If a circle is divided into three equal arcs, each is a major arc. (iv) A chord of a circle, which is twice as long as its radius, is a diameter of the circle.

What do equal chords make?

Converse theorem



And to do that, we will simply replace the equal chord with the equal arc. If the arcs are equal, then by definition so are their central angles, and the triangles are congruent by the Side-Angle-Side postulate. And as a result, the chords are equal as corresponding sides in congruent triangles.

What are circle chords?

The chord of a circle can be defined as the line segment joining any two points on the circumference of the circle. It should be noted that the diameter is the longest chord of a circle which passes through the center of the circle.

What does half a circle equal?

In mathematics (and more specifically geometry), a semicircle is a one-dimensional locus of points that forms half of a circle. The full arc of a semicircle always measures 180° (equivalently, π radians, or a half-turn).

Which is the biggest chord of a circle?

diameter

A chord that passes through the center of a circle is called a diameter and is the longest chord.

How do you find the chord of a circle?

Video quote: So any line segment you draw that touches both sides of a circle is a chord. You're probably familiar with a special chord the one that goes through the center.

Are radii chords?

Radius: A circle’s radius — the distance from its center to a point on the circle — tells you the circle’s size. In addition to being a measure of distance, a radius is also a segment that goes from a circle’s center to a point on the circle. Chord: A segment that connects two points on a circle is called a chord.

What are two chords in a circle?

Video quote: And we have two chords in the circle remember that a chord is basically just a line segment that's inside of the circle. That has its endpoints on the perimeter of the circle.

Are chords diameters?

Answer. Answer: Chord is a line that joins any two points on the circle but diameter is the line that passes through the centre of the circle joining any two points on the circle. So every chord of a circle is not the diameter but a diameter is the longest chord of the circle.

What is C chord?

The notes of a C major chord are the 1st (the root note), 3rd, and 5th notes, which are C (the root note), E and G. Notice that the octave (the 8th note) is also part of the chord. In fact, either of the notes C, E and G can be played in any octave on the guitar and it will still be called a C major chord.

Can a secant be a chord?

Secant of the Circle Definition



A straight line that intersects a circle in two points is called a secant line. A chord is the line segment that joins two distinct points of the circle. A chord is in a unique secant line and every secant line defines a unique chord.

Are all chords of a circle congruent?

If two chords define central angles equal in measure, then they are congruent. Theorems about chords and diameters in a circle and their converses: If a diameter of a circle bisects a chord, then it must be perpendicular to the chord. If a diameter of a circle is perpendicular to a chord, then it bisects the chord.

What is true about chords in a circle?

Which description is TRUE for chords of a circle? The diameter of a circle is the longest chord of that circle. O The radius of a circle is the shortest chord of the circle. O f two chords in a circle are parallel, they are congruent O Atangent to a circle is perpendicular to a chord at the point of intersection.

Can a chord go through the center of a circle?

A chord is a line segment whose endpoints are on a circle. If a chord passes through the center of the circle, it is called a diameter.

What are the 6 main circle theorems?

• Circle Theorem 1 – Angle at the Centre.
• Circle Theorem 2 – Angles in a Semicircle.
• Circle Theorem 3 – Angles in the Same Segment.
• Circle Theorem 4 – Cyclic Quadrilateral.
• Circle Theorem 5 – Radius to a Tangent.
• Circle Theorem 6 – Tangents from a Point to a Circle.
• Circle Theorem 7 – Tangents from a Point to a Circle II.

What are the 9 circle theorems?

Now for the theorems:

• The angle at the centre is twice the angle at the circumference.
• The angle in a semicircle is a right angle.
• Angles in the same segment are equal.
• Opposite angles in a cyclic quadrilateral sum to 180°
• The angle between the chord and the tangent is equal to the angle in the alternate segment.

What is theorem of a circle?

Circle Theorem. Circle theorem includes the concept of tangents, sectors, angles, the chord of a circle and proofs. A circle is the locus of all points in a plane which are equidistant from a fixed point.

What are the 8 theorems of a circle?

Technical note




• First circle theorem – angles at the centre and at the circumference.
• Second circle theorem – angle in a semicircle.
• Third circle theorem – angles in the same segment.
• Fourth circle theorem – angles in a cyclic quadlateral.
• Fifth circle theorem – length of tangents.

Why is the diameter the longest chord of the circle?

The diameter of a circle is considered to be the longest chord because it joins to points on the circumference of a circle. In the circle below, AB, CD, and EF are the chords of the circle.

Can a chord be shorter than a radius?

A chord can be shorter than a radius of the same circle. 6. A radius is always congruent to another radius of the same circle.