What are the 4 circle theorems?

Circle theorems: where do they come from?

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°

What are the 8 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.

What is a tangent point?

A tangent to a circle is a straight line which touches the circle at only one point. This point is called the point of tangency. The tangent to a circle is perpendicular to the radius at the point of tangency.

What is tangent formula?

The tangent of x is defined to be its sine divided by its cosine: tan x = sin x/ cos x.

What is tangent segment Theorem?

If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.

What is theorem 11 in geometry?

Theorem 11: If three parallel lines cut off equal segments on some transversal line, then they will cut off equal segments on any other transveral.

What is circle theorem?

Circle theorem may refer to: Thales’ theorem, if A, B and C are points on a circle where the line AC is a diameter of the circle, then the angle ∠ABC is a right angle. Alternate segment theorem.

How do you find the tangent line of a circle?

A tangent to a circle is a straight line which intersects (touches) the circle in exactly one point. To find the equation of tangent at the given point, we have to replace the following. x 2 = xx 1, y 2 = yy 1, x = (x + x 1)/2, y = (y + y 1)/2.

What is the tangent in an unit circle?

The tangent function is a periodic function which is very important in trigonometry. The simplest way to understand the tangent function is to use the unit circle. For a given angle measure θ draw a unit circle on the coordinate plane and draw the angle centered at the origin, with one side as the positive x -axis.

What is the tangent point of a circle?

Tangent to a Circle. A tangent to a circle is a straight line which touches the circle at only one point. This point is called the point of tangency. The tangent to a circle is perpendicular to the radius at the point of tangency.

What is the tangent chord theorem?

The alternate segment theorem (also known as the tangent-chord theorem) states that in any circle, the angle between a chord and a tangent through one of the end points of the chord is equal to the angle in the alternate segment. In the above diagram, the angles of the same color are equal to each other.