This GRE® quant practice question tests your understanding of properties of triangles in Geometry. Concepts tested include properties of right triangles, orthocenter and circumcenter of triangles. Also, basic properties of coordinate geometry including coordinates of mid point of a line segment, equation of a line, computing intercepts of a line and distance between two points … [Read more...] about Geometry Triangles – Circumcentre, Orthocentre

# GRE Geometry, Solid Geometry, Coordinate Geometry

## GRE Geometry – same base, same height

An equilateral triangle and a parallelogram lie on the same base and between the same parallel lines. The area of the parallelogram is 200*root(3) sq cm. What is the length of the side of the triangle?Explanation: Two triangles with the same base and between the same parallel lines will have equal areas. Likewise, a triangle and a parallelogram with the same base and between … [Read more...] about GRE Geometry – same base, same height

## GRE Geometry – Planet Circles

Consider a planet P1 (like earth) that is spherical in shape. It has an atmospheric layer around it that also takes the same shape as that of the planet. An adventurist launches a rocket from a neighboring planet P2 to this planet P1. The rocket cuts the atmospheric layer at point A, grazes the planet P1 and goes out of the atmospheric layer at point B. If AB = 100 km, what is … [Read more...] about GRE Geometry – Planet Circles

## GRE Geometry – Chords and Circles

A, B and C are three points on a circle. AB, BC and AC are three chords where AB = AC. If the maximum length of BC is 10 cm, what is the area of triangle ABC? Explanation: If BC, which is a chord, should have the maximum length then it should be the diameter. And since angle(BAC) is the angle subtended by the diameter at the circumference, it should be 90 degrees. And we … [Read more...] about GRE Geometry – Chords and Circles

## Solid Geometry – Sectors cones

A sector of a circle of radius 5 cm is recast into a right circular cone of height 4 cm. What is the volume of the cone so formed? Explanation: A sector of a circle with radius 5 cm will look something like this. When recast into a right-circular cone of height 4 cm it will look something like this. Hence, the radius of the sector becomes the … [Read more...] about Solid Geometry – Sectors cones