Circumcircle of a Triangle

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 form chords of the circle.

Hence, the centre of the circle is located at the point of intersection of the perpendicular bisectors of the sides of the triangle. This point is known as the circumcentre of the triangle. The radius of the circumcircle is equal to the distance between the circumcentre and any one of the three vertices of the triangle. The circumcentre of a triangle is equidistance from the three vertices. In each of the given figures, the circumcircle of ∆XYZ is the circle with centre O and radius equal to OX, or OY, or OZ.

If ∆XYZ is an acute-angled triangle, as in (i), the circumcentre lies inside the triangle.

Circumcentre Lies Inside the Triangle

If ∆XYZ is a right-angled triangle, as in (ii), the circumcentre lies on the hypotenuse of the triangle (since, the angle in a semicircle is a right angle).

Circumcentre Lies on the Hypotenuse of the Triangle

If ∆XYZ is an obtuse-angled triangle, as in (ii), the circumcircle lies outside the triangle.

Circumcircle Lies Outside the Triangle

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

  • Incircle of a Triangle |Incentre of the Triangle|Point of Intersection

    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

10th Grade Math

From Circumcircle of a Triangle to HOME PAGE

New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

Share this page: What’s this?