What is the circle theorem rule?

Opposite angles in a cyclic quadrilateral sum to 180°: Angle at B + angle at D = angle at C + angle at E = 180°

What is the theorem of touching circles?

Theorem: If two circles touch each other (externally or internally), then their point of contact lies on the straight line joining their centers.

What is the 6th theorem?

Theorem 6: Each exterior angle of a triangle is equal to the sum of the interior remote angles.

What happens when two circles touch each other?

Determining whether two circles touch each other Two circles will touch if the distance between their centres, , is equal to the sum of their radii, or the difference between their radii. The centre of one circle will lie on the other circle when d = r 1 or d = r 2 . Two circles are concentric when .

What is kissing tangent?

In geometry, tangent circles (also known as kissing circles) are circles in a common plane that intersect in a single point. There are two types of tangency: internal and external.

Who invented circle theorems?

Thales
The first theorems relating to circles are attributed to Thales around 650 BC. Book III of Euclid’s Elements deals with properties of circles and problems of inscribing and escribing polygons.

What is circle in calculus?

A circle is the set of all points that are equidistant from a center point. The general equation of a circle is ( x − h ) 2 + ( y − k ) 2 = r 2 where is the center of the circle and is the radius of the circle.

How do you know if a circle is inside a circle?

If this case happens, the sum of the distance between the centres and smaller radius is equal to the bigger radius, then obviously the smaller circle lies completely inside the circle, with touching the circumference.

What is a kissing circle?

Circles that are mutually tangent to each other are called “kissing circles” because they barely touch each other (or “kiss”) at one point.

What is Miquel’s six circles theorem?

Miquel’s six circles theorem states that if five circles share four triple-points of intersection then the remaining four points of intersection lie on a sixth circle.

What is the converse of the five circles theorem?

Then the second intersection points (other than A,B,C,D,E), namely the new points M,N,P,R and Q are concyclic (lie on a circle). See diagram. The converse result is known as the Five circles theorem .

What is Miquel’s Pivot theorem?

The Pivot Theorem for various triangles. Miquel’s theorem is a result in geometry, named after Auguste Miquel, concerning the intersection of three circles, each drawn through one vertex of a triangle and two points on its adjacent sides.

What is Miquel’s Pentagon theorem?

Miquel’s Pentagon Theorem. Miquel’s six circles theorem states that if five circles share four triple-points of intersection then the remaining four points of intersection lie on a sixth circle.

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