What happens if diameter is perpendicular to a chord?

If a diameter of a circle is perpendicular to a chord, then it bisects the chord. If two chords are congruent, then the center is equidistant from the two chords.

What is the perpendicular to a chord conjecture?

Explanation: The cord of a circle is a segment whose endpoints are on the circle. This conjecture states that the perpendicular bisector of any chord passes through the center of the circle.

What is the relationship between radius and diameter diameter and a chord?

The chord of a circle which passes through the centre of the circle is called the diameter of the circle. The diameter of a circle is the distance across a circle. The diameter is also the longest chord of a circle. Diameter of a circle d = 2r, where r is the radius of the circle.

When a radius is perpendicular to a chord What conclusion can you draw about the chord and radius?

If a diameter or radius is perpendicular to a chord, then it bisects the chord and its arc. If two chords are congruent, then their corresponding arcs are congruent. If a diameter or radius is perpendicular to a chord, then it bisects the chord and its arc.

When a diameter is drawn in a circle and is perpendicular to a chord The arc of the chord is bisected?

How do you prove a line is perpendicular to a chord?

Therefore, we can say that ∆OAX ≅ ∆OBX. This proves that the line drawn through the centre of a circle to bisect a chord is perpendicular to the chord. Hence, the converse of this theorem is proved….Proof:

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What is the relation between chord and diameter?

Chords are equidistant from the center if and only if their lengths are equal. Equal chords are subtended by equal angles from the center of the circle. A chord that passes through the center of a circle is called a diameter and is the longest chord of that specific circle.

How do you calculate the diameter of a circle from a chord?

r is the radius of the circle. c is the angle subtended at the center by the chord….Chord Length Formula.

Formula to Calculate Length of a Chord
Chord Length Using Perpendicular Distance from the Center Chord Length = 2 × √(r2 − d2)
Chord Length Using Trigonometry Chord Length = 2 × r × sin(c/2)

What conjecture can you make about the line drawn from the centre of the circle perpendicular to a chord?

Perpendicular line from circle centre bisects chord If a line is drawn from the centre of a circle perpendicular to a chord, then it bisects the chord.

What is the relationship between chord of a circle and a perpendicular to it from the circle?

What is the Relationship Between the Chord of a Circle and a Perpendicular to it from the Center? The perpendicular drawn from the center of a circle to a chord bisects the chord. In other words, a line drawn through the center of a circle to bisect a chord is perpendicular to the chord.