How do you determine if points lie on a circle?

If the distance is greater than the radius, the point lies outside. If it’s equal to the radius, the point lies on the circle. And if it’s less than the radius, you guessed it right, the point will lie inside the circle.

How do you prove a chord is a diameter?

Proof that the Longest chord of a circle is its Diameter:

1. Draw circle O and any chord AB on it.
2. From one endpoint of the chord, say A, draw a line segment through the centre. That is, draw a diameter.
3. Now draw a radius from centre O to B.
4. By the triangle inequality,

Is AB the diameter of the circle?

In figure, AB is a diameter of the circle, CD is a chord equal to the radius of the circle.

How do you plot points on a circle?

Center away from the origin

1. Locate the center of the circle from the equation (h, v). Place the center of the circle at (3, –1).
2. Calculate the radius by solving for r.
3. Plot the radius points on the coordinate plane.
4. Connect the dots to the graph of the circle with a round, smooth curve.

How do you find the center and radius of two points?

A common form to write the equation of a circle in is the center-radius form. The center-radius form is: (x−h)2+(y−k)2=r2 Here, the center point is denoted by (h,k) and r is the radius of the circle.

What are circle chords?

A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. More generally, a chord is a line segment joining two points on any curve, for instance, an ellipse. A chord that passes through a circle’s center point is the circle’s diameter.

What is the radius of a circle whose diameter is given as 24cm?

∴ The radius of a circle of diameter 24 cm is 12 cm.

What is the perimeter of a quadrant of circle?

A quadrant of a circle is a sector of the circle whose sectorial angle is 90 degree. The perimeter of a quadrant of the circle is one fourth of the circumference and 2 times of the radius of the circle.

How do you show something as diameter?

The symbol or variable for diameter, ⌀, is sometimes used in technical drawings or specifications as a prefix or suffix for a number (e.g. “⌀ 55 mm”, indicating that it represents diameter).

What is the chord of a circle in math?

Chord of a Circle Definition. 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. The figure below depicts a circle and its chord.

What is the angle subtended by the chord of a circle?

If the endpoints of the chord CD are joined to the point P, then the angle ∠CPD is known as the angle subtended by the chord CD at point P. The angle ∠CQD is the angle subtended by chord CD at Q. The angle ∠COD is the angle subtended by chord CD at the center O. There are two basic formulas to find the length of the chord of a circle which are:

What are the basic theorems on chords and arcs of a circle?

Theorem 10: If the line segment joining any two points subtends equal angles at two other points that are on the same side, they are concyclic. This means that they all lie on the same circle. These are some of the basic theorems on the chords and arcs of a circle. We will read about some other theorems in the next chapter.

What does AB and CD mean in math?

The figure below depicts a circle and its chord. In the given circle with ‘O’ as the center, AB represents the diameter of the circle (longest chord), ‘OE’ denotes the radius of the circle and CD represents a chord of the circle.