In a cyclic quadrilateral ABCD, the diagonals intersect at E. If AE = 4 and EC = 9, what is the minimum length of diagonal BD? Answer: 12 Explanation We know that when two chords of a circle intersect at a point, AE*EC = BE*ED Hence, BE*ED = 4*9 = 36. Given the product of two quantities their sum is minimum when the two quantities are equal. Hence … [Read more...] about Cyclic Quadrilateral Circles

# GRE Geometry, Solid Geometry, Coordinate Geometry

## Quantitative Comparison – Coordinate Geometry

Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the following four answer choices:(A) Quantity A is greater.(B) Quantity B is greater.(C) The two quantities are equal.(D) The relationship cannot be determined from the information given.A circle with radius 5 and passing through the … [Read more...] about Quantitative Comparison – Coordinate Geometry

## More Than 1 Answer: Circles and Chords

What is the distance between two parallel chords of lengths 32 cm and 24 cm in a circle of radius 20 cm? Indicate ALL possible distances a) 1 b) 7 c) 4 d) 28 e) 2 f) 14 Solution: (C), (D) Explanation The two parallel chords can either both be on one side of the centre or on either sides of the centre of the circle. Case i: The two chords … [Read more...] about More Than 1 Answer: Circles and Chords

## Geometric Sequence – Triangles

One side of an equilateral triangle is 2 cms. The mid-points of its sides are joined to form another triangle whose mid-points are joined to form still another triangle. This process continues indefinitely. (i) Find the sum of the perimeters of all the triangles. (a) Cannot be determined (b) 4 (c) 12 (d) 8 (e) 10 Bonus Question (ii) Find the sum of the areas … [Read more...] about Geometric Sequence – Triangles