CAT Geometry Sectional Test 2 – with Solutions

CAT Quant Geometry Practice Test 2: Polygons, Circles and Solids

Working with triangle centres, cyclic quadrilaterals and solid figures is the core skill built by CAT Geometry Sectional Test 2, a CAT Quantitative Aptitude practice set. It also covers regular polygons, coordinate geometry and regions defined by linear inequalities. Aptitude360 gives a step-by-step solution for each problem.

What this CAT geometry practice set tests

• Triangles: incentre and centroid positions, altitude to the hypotenuse, integer-sided right triangles, area division by intersecting cevians
• Circles: intersecting chords, arcs in a given ratio, incircle of a right triangle, three mutually touching circles
• Quadrilaterals and polygons: area of a cyclic quadrilateral from its sides, regular hexagon and octagon areas, midpoint quadrilaterals
• Coordinate geometry: points equidistant from two given points, area of a region bounded by inequalities
• Mensuration: largest cone carved from a cuboid, balls displacing water in a jar, solid formed by rotating a triangle, percentage change in cylinder dimensions

Important formulas and rules for this set

• Intersecting chords: \( AP\times PB=CP\times PD \)
• Cyclic quadrilateral area: \( \sqrt{(s-a)(s-b)(s-c)(s-d)} \)
• Incentre x-coordinate: \( x=\dfrac{ax_{1}+bx_{2}+cx_{3}}{a+b+c} \)
• Altitude to hypotenuse: \( AD^{2}=BD\times DC \)
• Volume of a cone: \( V=\dfrac{1}{3}\pi r^{2}h \)
• Regular hexagon of side a: \( \dfrac{3\sqrt{3}}{2}a^{2} \)

Preparation tips for CAT geometry and mensuration

• For any point inside an equilateral triangle, the three perpendicular distances to the sides add up to the height. Use this before attempting heavy algebra.
• For inequality regions, plot each boundary line, find the corner points and split the region into triangles.
• In carving problems, test each face of the cuboid as the base of the cone and compare the volumes.

Who this sectional test suits

It suits CAT aspirants in the practice stage who already know the standard geometry results and want to apply them in less familiar settings.