*Monday, July 27th, 2020*

In the previous post we discussed lines, triangles, parallelograms, trapeziums, polygons etc. Now, we will discuss other expanses of geometry which are vital as, the questions on these topics are asked repeatedly in CAT. Let us look at few of the fundas / formulae on these topics that are often neglected by students and can fetch some crucial marks in the exam.

**Funda 1:** Angle made by Secants

2 .

In both these cases, PA * PB = PC * PD

**Funda 2:** Common Tangents

eg:

Note: The two centers(O and O’), point of intersection of DCTs (P)and point of intersection of TCTs (Q) are collinear. Q divides OO’ in the ratio r_{1} : r_{2} internally whearea P divides OO’ in the ratio r_{1} : r_{2} externally.

**Funda 4:** Co-ordinate Geometry

- The X axis divides the line joining P(x
_{1},y_{1}) and Q(x_{2},y_{2}) in the ratio of y_{1}: y_{2} - The Y axis divides the line joining P(x
_{1},y_{1}) and Q(x_{2},y_{2}) in the ratio of x_{1}: x_{2} - If we know three points A(x
_{1},y_{1}), B(x_{2},y_{2}) and C(x_{3},y_{3}) of a parallelogram, the fourth point is given by

- (x
_{1}+ x_{3 }– x_{2}, y_{1}+ y_{3 }– y_{2})

With this I will like to wrap up this post on Geometry. Best of Luck to all of you for CAT!

Geometry Fundas for CAT Quantitative Aptitude Preparation – Part 1

Geometry Basics for CAT – Triangle related questions and problems

Mensuration Basics and 3-Dimensional Geometry Concepts for CAT

All questions from CAT Exam Quantitative Aptitude – Geometry

Quantitative Aptitude – Geometry – Triangles – Q1: Let P be an interior point of a right-angled isosceles triangle ABC with hypotenuse AB.

Quantitative Aptitude – Geometry – Triangles – Q2: Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 km, respectively.

Quantitative Aptitude – Geometry – Triangles – Q3: From a triangle ABC with sides of lengths 40 ft, 25 ft and 35 ft, a triangular portion GBC is cut off where G is the centroid of ABC.

Quantitative Aptitude – Geometry – Circles – Q1: ABCD is a quadrilateral inscribed in a circle with centre O. If ∠COD = 120 degrees and ∠BAC = 30 degrees

Quantitative Aptitude – Geometry – Circles – Q2: Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with diameter BC.

Quantitative Aptitude – Geometry – Coordinate – Q1: The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is

Quantitative Aptitude – Geometry – Coordinate – Q2: The shortest distance of the point (½, 1) from the curve y = |x -1| + |x + 1| is

Quantitative Aptitude – Geometry – Mensuration – Q1: The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm

Quantitative Aptitude – Geometry – Mensuration – Q2: A ball of diameter 4 cm is kept on top of a hollow cylinder standing vertically.

Quantitative Aptitude – Geometry – Mensuration – Q3: A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio 1 : 1 : 8: 27: 27.

Quantitative Aptitude – Geometry – Polygon – Q1: Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is

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