CAT Geometry Short Notes: Chapter-wise Weightage and Solved Questions

    CAT Geometry: 5 chapters, 0 practice questions and one solved question from each chapter.

    Geometry Chapter Matrix

    ChapterPYQsShare of unit PYQsPractice questions
    Circles, Chords, Tangents and Incircles00%0
    Coordinate Geometry, Loci and Analytic Regions00%0
    Mensuration, 3D and Optimization00%0
    Quadrilaterals, Polygons and Area Ratios00%0
    Triangles, Similarity, Medians and Altitudes00%0

    One Solved Question from Each Geometry Chapter

    Question 1 · Quantitative Ability MCQ

    Three identical circles of radius cm touch each other externally. A smaller circle is placed in the central gap so that it touches all three circles externally. What is its radius, in cm?

    1. A.

      2√3 - 3

    2. B.

      3 - 2√3

    3. C.

      2√3 + 3

    4. D.

      6 - 2√3

    Correct Answer:

    A

    Step-by-Step Solution

    Key idea: inner circle in the symmetric gap between three equal touching circles.

    Step 1: Centres of the three given circles form an equilateral triangle of side

    Step 2: The gap circle centre is the triangle centre. Distance from triangle centre to a vertex is the circumradius:

    Step 3: If the small radius is , external touch gives

    Step 4: Solve:

    Answer: Option A.

    Trap: using subtraction here belongs to the outer enclosing circle case. The inner gap circle touches externally, so radii add.

    chapter
    CAT Geometry Short Notes: Chapter-wise Weightage and Solved Questions

    CAT Geometry: 5 chapters, 0 practice questions and one solved question from each chapter.

    A question from this chapter

    Question 1

    Three identical circles of radius cm touch each other externally. A smaller circle is placed in the central gap so that it touches all three circles externally. What is its radius, in cm?

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