CAT Geometry Previous Year Questions (PYQs): Chapter-wise Weightage and Solved Questions

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

Geometry Chapter Matrix

Chapter	PYQs	Share of unit PYQs	Practice questions
Circles, Chords, Tangents and Incircles	0	0%	0
Coordinate Geometry, Loci and Analytic Regions	0	0%	0
Mensuration, 3D and Optimization	0	0%	0
Quadrilaterals, Polygons and Area Ratios	0	0%	0
Triangles, Similarity, Medians and Altitudes	0	0%	0

Circles, Chords, Tangents and Incircles Previous Year Questions (PYQs) (9 questions)
Coordinate Geometry, Loci and Analytic Regions Previous Year Questions (PYQs) (3 questions)
Mensuration, 3D and Optimization Previous Year Questions (PYQs) (1 questions)
Quadrilaterals, Polygons and Area Ratios Previous Year Questions (PYQs) (11 questions)
Triangles, Similarity, Medians and Altitudes Previous Year Questions (PYQs) (7 questions)

One Solved Question from Each Geometry Chapter

Question 1 · Quantitative Ability NAT

Two tangents drawn from a point P and a circle with center O at point Q and R. Point A and B lie on PQ and PR, repectively, such that AB is also a tangent to the same circle. If $∠ A O B = 5 0^{\circ}$ , then $∠ A P B$ , in degrees equals

Correct Answer:

Step-by-Step Solution

Let the circle be tangent to $P Q$ at $Q$ , $P R$ at $R$ , and $A B$ at $C$ . Tangents from an external point to a circle are equal in length, and the line from the center to the external point bisects the angle between the tangents. Thus, $O A$ bisects $∠ QO C$ and $O B$ bisects $∠ R O C$ . The angle $∠ A O B = ∠ A O C + ∠ B O C = \frac{1}{2} ∠ QO C + \frac{1}{2} ∠ R O C = \frac{1}{2} ∠ QO R$ . Given $∠ A O B = 5 0^{\circ}$ , we have $\frac{1}{2} ∠ QO R = 5 0^{\circ}$ , so $∠ QO R = 10 0^{\circ}$ . In the quadrilateral $P QO R$ , the angles at $Q$ and $R$ are $9 0^{\circ}$ because the radius is perpendicular to the tangent at the point of contact. The sum of angles in a quadrilateral is $36 0^{\circ}$ , so $∠ QP R + ∠ QO R = 18 0^{\circ}$ . Therefore, $∠ A P B = ∠ QP R = 18 0^{\circ} - 10 0^{\circ} = 8 0^{\circ}$ .

chapter

CAT Geometry Previous Year Questions (PYQs): 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

Two tangents drawn from a point P and a circle with center O at point Q and R. Point A and B lie on PQ and PR, repectively, such that AB is also a tangent to the same circle. If ∠ A O B = 5 0^{\circ}, then ∠ A P B, in degrees equals

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