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CAT Geometry Sectional Test 1 – with Solutions

A CAT Quant geometry practice set covering triangle theorems, circle tangents, regular polygons, coordinate geometry and applied mensuration, with worked solutions throughout.

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Questions
22
Duration
40 min
Marks
66

Negative marking

Attempts
100
Access
With a course
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Real test conditions

Before you launch the test

This is the computer-based test format, not a quiz page: one clock, a question palette, and no way back once a section closes. Read these first.

  • It runs in full screen. The test takes over the screen when it starts, the way the real computer-based test does.
  • Leaving it is counted. Switching away is recorded and warned about; the third time, the paper is submitted for you.
  • The clock runs for 40 minutes. Set aside that long, uninterrupted. It starts when you begin, keeps running if you close the tab, and submits the paper at zero.

About this test

CAT Geometry Mock Test 1: Triangles, Circles and Mensuration Practice

CAT Geometry Sectional Test 1 is a Quantitative Aptitude practice set for CAT covering triangles, circles, polygons, coordinate geometry and mensuration. It combines classic theorem-based problems with applied ones on buckets, towers and rolled sectors. Aptitude360 provides a step-by-step solution to every problem in the set.

Topics covered in this CAT Geometry set

  • Triangles: angle bisector theorem, bisector length with a given vertex angle, area from the lengths of the medians, shortest altitude from three sides
  • Area ratios when two cevians of a triangle intersect, and triangles formed by the diagonals of a trapezium
  • Circles: tangent and secant from an external point, direct common tangents, tangents to a cyclic quadrilateral, circles touching externally
  • Polygons: interior and exterior angle relations, counting triangles formed from the vertices of a regular polygon
  • Coordinate geometry: perpendicular distance from a point to a line, section formula, squares built on two given points
  • Mensuration: frustum-shaped bucket, sector rolled into a cone, recasting a melted cylinder, rhombus diagonals
  • Heights and distances: angle of elevation of a tower, crossed wires between two poles

Key geometry formulas to revise for this test

  • Angle bisector theorem: \( \dfrac{BD}{DC}=\dfrac{AB}{AC} \)
  • Bisector of angle A: \( AD=\dfrac{2bc\cos(A\div2)}{b+c} \)
  • Area from medians: \( \Delta=\dfrac{4}{3}\times\Delta_{\text{medians}} \)
  • Tangent and secant: \( PT^{2}=PA\times PB \)
  • Interior angle of a regular n-gon: \( \dfrac{(n-2)\times180^{\circ}}{n} \)
  • Point to line: \( d=\dfrac{|ax_{1}+by_{1}+c|}{\sqrt{a^{2}+b^{2}}} \)

Revision tips for CAT geometry problems

  • Draw a neat, roughly proportional figure before you calculate, especially for bisector and tangent problems where a wrong sketch easily misleads.
  • For two crossed wires between poles, remember that the crossing height depends only on the pole heights, not on the distance between them.
  • When a sector is rolled into a cone, equate the arc length to the circumference of the base and the sector radius to the slant height.

Who this geometry sectional suits

CAT and other MBA entrance aspirants who have finished the basic geometry theory and want to test it on mixed, exam-style problems.

FAQs about CAT Geometry Sectional Test 1 – with Solutions

What is the angle bisector theorem in geometry?
The bisector of an angle of a triangle divides the opposite side in the ratio of the two sides containing that angle. For example, if AD bisects angle A, then BD is to DC as AB is to AC.
How do you find the area of a triangle from its medians?
Find the area of a triangle whose sides equal the three medians, using Heron's formula. The original triangle's area is four thirds of that value.
What is the tangent secant theorem?
If a tangent PT and a secant PAB are drawn from an external point P, then the square of PT equals PA multiplied by PB.
How do you find the interior angle of a regular polygon?
Each exterior angle of a regular polygon with n sides is 360 degrees divided by n. The interior angle is 180 degrees minus that exterior angle.

Test structure

How the paper is split, and how long each part runs. A section you have finished cannot be returned to.

SectionQuestionsTime
CAT Geometry Sectional Test - 12240 min

Marking & rules

Total marks
66 across 22 questions.
Negative marking
A wrong answer costs marks. Leaving a question unanswered costs nothing.
Attempts
100 in total. An attempt is spent the moment you begin one.

What you get when you submit

The analysis is ready the moment you submit the paper.

Score and accuracy

Marks, percentage, right, wrong and skipped, and the time you took.

Section by section

The same figures for each section, so a weak one cannot hide in an average.

The full answer key

Every question with your answer, the right one, the working, and the video where there is one.

Where you stand

Your score against the spread of everyone else who has sat this test.

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