If the circumcentre of a triangle lies outside it, then the triangle is

Options

A. Equilateral
B. Acute angled
C. Right angled
D. Obtuse angled

Answer

To determine the type of triangle for which the circumcenter lies outside the triangle, we can follow these steps:

### Step 1: Understanding the Circumcenter
The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. It is also the center of the circumcircle, which is the circle that passes through all three vertices of the triangle.

**Hint:** Remember that the circumcenter's position relative to the triangle can vary depending on the type of triangle.

### Step 2: Analyzing Different Types of Triangles
1. **Acute Triangle**: In an acute triangle, all angles are less than 90 degrees. The circumcenter lies inside the triangle.
2. **Right Triangle**: In a right triangle, the circumcenter is located at the midpoint of the hypotenuse, which is also inside the triangle.
3. **Obtuse Triangle**: In an obtuse triangle, one angle is greater than 90 degrees. The circumcenter lies outside the triangle.

**Hint:** Consider the angles of the triangle to determine the location of the circumcenter.

### Step 3: Conclusion
From the analysis, we conclude that if the circumcenter of a triangle lies outside the triangle, then the triangle must be an **obtuse triangle**.

**Final Answer:** The triangle is an obtuse triangle.