In triangle LMN, ∠L = 85° and ∠M = 85°. Where is the circumcentre located ?
Inside the triangle
The sum of angles in triangle LMN is \(180^\circ\), so \(\angle N = 180^\circ - 85^\circ - 85^\circ = 10^\circ\).
All three angles, \(85^\circ\), \(85^\circ\), and \(10^\circ\), are less than \(90^\circ\), so triangle LMN is an acute-angled triangle.
For an acute-angled triangle, the circumcentre always lies inside the triangle.
Hence, the circumcentre of triangle LMN is located inside the triangle.
Similar Questions
In triangle ABC, ∠A = 58° and ∠C = 62°. If O is the circumcentre, find ∠AOC.
A triangular board has sides 9 cm, 10 cm, and 17 cm. A circle passes through all three vertices. Find the circumradius.
Important Questions from Geometry
If the angles of a triangle are in the ratio of 2:3:4, then the difference of the measure of greatest angle and smallest angle is
In ΔABC, ∠A = 90°, AD ┴ BC and AD = BD = 2 cm. The length of CD is
How many lines of symmetry does a rectangle have?
The number of diagonals in each face a cube is
Which of the following is/are the geometric figures with the line of symmetry?
I. Rectangle
II. Isosceles triangle
