Statement 1 - Let O be the orthocentre of $△ A BC$ and $O A = \frac{a}{2 s i n A}$ , then the triangle ABC is an isosceles triangle.

Statement 2 - The orthocentre of a triangle is the point of intersection of the altitudes.

Question

Statement 1 - Let O be the orthocentre of $△ A BC$ and $O A = \frac{a}{2 s i n A}$ , then the triangle ABC is an isosceles triangle.

Statement 2 - The orthocentre of a triangle is the point of intersection of the altitudes.

TestHub · Accepted Answer

O A = 2 R cos A while 2 s i n A a ​ = R , so cos A = 2 1 ​ , i.e. A = 6 0 ∘ only. That does not make the triangle isosceles, so Statement 1 is false. Statement 2 is true.

Mathematics - Properties of Triangle Question with Solution | TestHub

Options:

Doubts & Discussion