How many Circles questions come in CAT Quant?

About 0.4 questions in a 22-question Quant section, worth roughly 1 marks. Circles appeared in 13 of the 24 CAT papers from 2017 to 2025, 16 questions in all, which ranks it 21 of 25 Quant chapters.

Are Circles questions in CAT MCQ or TITA?

19% of the Circles questions asked since 2017 were TITA (type in the answer, no negative marking). The rest were multiple choice.

What types of Circles questions does CAT ask?

CAT keeps returning to 5 question shapes in Circles: The area of a curved region; A chord, and its distance from the centre; Angles in a circle; Circles that touch each other; Tangents, or intersecting chords.

Circles for CAT: Formulas, Weightage & Question Types

Curved areas, chords, angles in a circle, tangents and touching circles.

Circles formula sheet

Everything CAT needs from Circles, in one place. Bookmark it for revision; the lesson in the app explains where each line comes from and when to reach for it.

Everything for this chapter, in one place. $r$ is the radius, $\theta$ an angle at the centre in degrees.

Basics


Circumference	$2\pi r$
Area	$\pi r^2$
Arc length	$\dfrac{\theta}{360} \times 2\pi r$
Sector area	$\dfrac{\theta}{360} \times \pi r^2$
Segment area	sector $-$ triangle
Triangle inside a sector	$\dfrac{1}{2}r^2\sin\theta$

Chords


The perpendicular from the centre	bisects the chord
So, with $d$ the distance from the centre	$\left(\dfrac{\text{chord}}{2}\right)^2 + d^2 = r^2$
Chord from the central angle	$2r\sin\dfrac{\theta}{2}$
Equal chords	are equidistant from the centre
Intersecting chords at $E$	$AE \times EB = CE \times ED$

Angles


Angle at the centre	twice the angle at the circumference on the same arc
Angle in a semicircle	$90^\circ$
Angles in the same segment	are equal
Cyclic quadrilateral	opposite angles add to $180^\circ$

Tangents


A tangent	is perpendicular to the radius at the point of contact
Two tangents from one point	are equal in length
Length of a tangent from distance $d$	$\sqrt{d^2-r^2}$
Two tangents meeting at angle $2\theta$	the point is at $\dfrac{r}{\sin\theta}$ from the centre
With an inner tangent line $AB$	$\angle AOB = 90^\circ - \dfrac{\angle APB}{2}$

Touching circles


Touching externally	centres are $r_1+r_2$ apart
Touching internally	centres are $\lvert r_1-r_2 \rvert$ apart
Three circles on a common tangent line	$\dfrac{1}{\sqrt{r_3}} = \dfrac{1}{\sqrt{r_1}} + \dfrac{1}{\sqrt{r_2}}$
Three equal circles of radius $r$ , mutually touching	the enclosing circle has $r\left(1+\frac{2}{\sqrt3}\right)$ , the inner one $r\left(\frac{2}{\sqrt3}-1\right)$

The 5 Circles question types CAT repeats

Past CAT papers return to the same few shapes. Learn to recognise them and most questions become a known routine.

01
The area of a curved region
02
A chord, and its distance from the centre
03
Angles in a circle
04
Circles that touch each other
05
Tangents, or intersecting chords

Is Circles costing you marks?

Take the free diagnostic to see where you stand in Circles and every other high-weight chapter, then learn, practise and prove it on fresh questions.

Take the free diagnostic

No sign-up needed. Your first chapter is free end to end.

Circles in CAT: quick answers

How many Circles questions come in CAT Quant?: About 0.4 questions in a 22-question Quant section, worth roughly 1 marks. Circles appeared in 13 of the 24 CAT papers from 2017 to 2025, 16 questions in all, which ranks it 21 of 25 Quant chapters.
Are Circles questions in CAT MCQ or TITA?: 19% of the Circles questions asked since 2017 were TITA (type in the answer, no negative marking). The rest were multiple choice.
What types of Circles questions does CAT ask?: CAT keeps returning to 5 question shapes in Circles: The area of a curved region; A chord, and its distance from the centre; Angles in a circle; Circles that touch each other; Tangents, or intersecting chords.

Circles for CAT: Formulas, Weightage & Question Types

Circles formula sheet

The 5 Circles question types CAT repeats

Is Circles costing you marks?

Circles in CAT: quick answers

More Geometry for CAT