Incircle of a Triangle

We will discuss here the Incircle of a triangle and the incentre of the triangle.

The circle that lies inside a triangle and touches all the three sides of the triangle is known as the incircle of the triangle.

If all the three sides of a triangle touch a circle then the sides of the triangle are tangents to the circle. Hence, the centre of the circle is located at the point of intersection of the internal bisectors of the angles of the triangle. This point is called the incentre of the triangle and is equidistant from the sides of the triangle.

The radius of this circle is equal to the shortest (perpendicular) distance between the incentre and any one of the sides.

$Incircle of a Triangle$

Here, the incircle of ∆XYZ is the circle with centre O and radius equal to OA, or OB, or OC.

Also, XB = XC, YA = YB and ZA = ZC.

You might like these

Problems on Relation Between Tangent and Secant | Square of Tangent

Here we will solve different types of Problems on relation between tangent and secant. 1. XP is a secant and PT is a tangent to a circle. If PT = 15 cm and XY = 8YP, find XP. Solution: XP = XY + YP = 8YP + YP = 9YP. Let YP = x. Then XP = 9x. Now, XP × YP = PT^2, as the
Problems on Two Tangents to a Circle from an External Point | Diagram

We will solve some Problems on two tangents to a circle from an external point. 1. If OX any OY are radii and PX and PY are tangents to the circle, assign a special name to the quadrilateral OXPY and justify your answer. Solution: OX = OY, are radii of a circle are equal.
Solved Examples on the Basic Properties of Tangents | Tangent Circle

The solved examples on the basic properties of tangents will help us to understand how to solve different type problems on properties of triangle. 1. Two concentric circles have their centres at O. OM = 4 cm and ON = 5 cm. XY is a chord of the outer circle and a tangent to
Circumcentre and Incentre of a Triangle | Radius of Circumcircle

We will discuss circumcentre and incentre of a triangle. In general, the incentre and the circumcentre of a triangle are two distinct points. Here in the triangle XYZ, the incentre is at P and the circumcentre is at O. A special case: an equilateral triangle, the bisector
Circumcircle of a Triangle | Circumcentre of the Triangle | Diagram

We will discuss here the Circumcircle of a Triangle and the circumcentre of a triangle. A tangent that passes through the three vertices of a triangle is known as the circumcircle of the triangle. When the vertices of a triangle lie on a circle, the sides of the triangle