Revision: Geometry >> Constructions Maths (English Medium) ICSE Class 10 CISCE

A circumcircle is a circle that passes through all three vertices of a triangle. The three vertices lie on the boundary of the circle.

The circumcenter is the center point of the circumcircle. It is the unique point where all three perpendicular bisectors of the triangle's sides meet.

• The circumcenter is equidistant from all three vertices of the triangle.

The circumradius is the radius of the circumcircle. It is the distance from the circumcenter to any vertex of the triangle.

The In-Circle of a triangle is the largest possible circle that can be drawn inside the triangle such that it just touches (is tangent to) all three sides.

The point where all three angle bisectors of a triangle meet. This point is the center of the In-Circle.

The perpendicular distance from the Incenter (I) to any of the three sides. This distance is the radius of the In-Circle.

\[\frac{(2n-4)}{n}\times90^\circ\]

• The tangent at any point of a circle is perpendicular to the radius at the point of contact.
• Angle in a semicircle is 90°

• From an external point, only two tangents can be drawn to a circle.

• Tangents from an external point are equal in length.

• A tangent is perpendicular to the radius at the point of contact.