In a right-angled triangle, the Orthocenter lies at which of the following points?
The vertex of the right angle.
The orthocentre of a triangle is the point where all three altitudes meet. An altitude is the perpendicular dropped from a vertex to the opposite side.
Consider a right-angled triangle with the right angle at vertex \(C\), and legs \(CA\) and \(CB\) meeting at \(C\).
The altitude from \(A\) must be perpendicular to side \(CB\). But \(CA\) is already perpendicular to \(CB\) (right angle at \(C\)), so the leg \(CA\) itself is the altitude from \(A\) — it passes through \(C\).
Likewise, the altitude from \(B\) is the leg \(CB\), which also passes through \(C\). So two altitudes meet exactly at the right-angle vertex \(C\).
Hence, in a right-angled triangle the orthocentre lies at the vertex of the right angle.
Similar Questions
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Important Questions from Geometry
ABCDEF is a regular hexagon. Side of the hexagon is 36 cm. What is the area of the triangle AOB ?
If ∆ABC ~ ∆DEF, and BC = 4 cm, EF = 5 cm and the area of triangle ABC = 80 cm 2, then the area of the triangle DEF is:
If Δ ABC is right angled at B, AB = 12 cm and ∠CAB = 60°, determine the length of BC.
If ΔABC and ΔDEF are congruent triangles, then which of the following is FALSE?
D and E are points on the sides AB and AC, respectively, of ΔABC such that DE is parallel to BC and AD ∶ DB = 7 ∶ 9. If CD and BE intersect each other at F. then find the ratio of areas of ΔDEF and ΔCBF.
