## How can you prove that two circles are orthogonal?

Two curves are said to be orthogonal if their angle of intersection is a right angle i.e the tangents at their point of intersection are perpendicular.

## What is the condition of orthogonality of circle?

Two circles are said to be orthogonal circles, if the tangent at their point of intersection are at right angles. If two circles are cut orthogonally then it must satisfy the following condition. are orthogonal. The two circles cut orthogonally and hence they are orthogonal circles.

How do you show two circles intersect at right angles?

Perpendicular (Orthogonal) Circles If two circles intersect in two points, and the radii drawn to the points of intersection meet at right angles, then the circles are orthogonal, and the circles can be said to be perpendicular to each other.

What do you mean by orthogonal circles?

Orthogonal circles are orthogonal curves, i.e., they cut one another at right angles. By the Pythagorean theorem, two circles of radii and whose centers are a distance apart are orthogonal if. (1) Two circles with Cartesian equations.

### What is orthogonal in maths?

Orthogonal is commonly used in mathematics, geometry, statistics, and software engineering. Most generally, it’s used to describe things that have rectangular or right-angled elements. More technically, in the context of vectors and functions, orthogonal means “having a product equal to zero.”

### How do you find the point of contact between two circles?

External and Internal Contacts of Circles. If two circles with centres C1(x1, y1) and C2(x2, y2) and radii r1 and r2 respectively, touch each other externally, C1C2 = r1 + r2. Coordinates of the point of contact are. C1C2 = r1- r2.

What is a common chord of two circles?

A line joining common points of two intersecting circles is called common chord. AB is common chord.

What is meant by orthogonal?

1a : intersecting or lying at right angles In orthogonal cutting, the cutting edge is perpendicular to the direction of tool travel. b : having perpendicular slopes or tangents at the point of intersection orthogonal curves.

#### What is orthogonal method?

An orthogonal method is an additional method that provides very different selectivity to the primary method. The orthogonal method can be used to evaluate the primary method.

What do you call overlapping circles?

A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things. Circles that overlap have a commonality while circles that do not overlap do not share those traits. Venn diagrams help to visually represent the similarities and differences between two concepts.

Which is the center of an orthogonal circle?

If a circle with center cuts any one of the three circles orthogonally, it cuts all three orthogonally. This circle is called the orthogonal circle (or radical circle) of the system. The orthogonal circle is the locus of a point whose polars with respect to the three given circles are concurrent (Lachlan 1893, p. 237).

## How are two orthogonal circles of radii related?

By the Pythagorean theorem, two circles of radii and whose centers are a distance apart are orthogonal if A theorem of Euclid states that, for the orthogonal circles in the above diagram, (Dixon 1991, p. 65). The radical lines of three given circles concur in the radical center .

## Which is an example of an orthogonal curve?

Orthogonal circles are orthogonal curves, i.e., they cut one another at right angles. By the Pythagorean theorem, two circles of radii and whose centers are a distance apart are orthogonal if