How Do You Prove A Circle?

What are the 8 circle theorems?

This collection holds dynamic worksheets of all 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.More items….

What are the six circle theorems?

In geometry, the six circles theorem relates to a chain of six circles together with a triangle, such that each circle is tangent to two sides of the triangle and also to the preceding circle in the chain. The chain closes, in the sense that the sixth circle is always tangent to the first circle.

How many circles can be drawn around a circle touching it?

The only answer to this question is “Infinite”. Circle has a fixed point known as its centre. And infinite number of circles can be drawn by keeping this point as the centre. And there is nothing called as a circle with zero radius.

Are chords in a circle equal?

Among properties of chords of a circle are the following: 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.

What is the radius of a circle?

In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the Latin radius, meaning ray but also the spoke of a chariot wheel.

How many angles are in a circle?

360 degreesA circle has a total of 360 degrees all the way around the center, so if that central angle determining a sector has an angle measure of 60 degrees, then the sector takes up 60/360 or 1/6, of the degrees all the way around.

How do you prove triangles are similar in a circle?

Two triangles in a circle are similar if two pairs of angles have the same intercepted arc. Sharing an intercepted arc means the inscribed angles are congruent. Since these angles are congruent, the triangles are similar by the AA shortcut.

What are the circle theorems rules?

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°The angle between the chord and the tangent is equal to the angle in the alternate segment.More items…