Area of a Triangle

Solution:

Geometry: Problem involving orthocentre

ABC  is a triangle with AB = 13; BC = 14 and CA = 15. AD and BE  are the altitudes from A and B  to BC and AC respectively. H is the point of intersection of AD and BE. Find the ratio HD/HB. 

Solution: 

Cone on a Sphere : Geometry

A hollow right circular cone rests on a sphere as shown in the figure. The height of the cone is 4 metres and the radius of the base is 1 metre. The volume of the sphere is same as that of the cone. What is the distance between the centre of the sphere and the vertex of the cone?

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