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CAT Circles questions with solutions

Chords, tangents and circle geometry. 18 questions from our 2016–2025 CAT pattern papers. Each has the answer and a full solution.

Also practise: Circles for NDA

CAT 2025

Find the length of their direct common tangent.CAT 2025 Slot 1 · hard
Two chords AB and CD of a circle intersect at an interior point P. AP = 6 cm, PB = 8 cm and CP = 4 cm. Find the length of PD (in cm).CAT 2025 Slot 3 · medium

CAT 2024

Two circles, each of radius 5 cm, have their centres 6 cm apart. Find the length of their common chord (in cm).CAT 2024 Slot 1 · medium

CAT 2023

Two parallel chords of a circle of radius 13 cm, lying on the same side of the centre, have lengths 24 cm and 10 cm. Find the distance between the…CAT 2023 Slot 2 · medium

CAT 2022

A chord of a circle of radius 13 cm is at a perpendicular distance of 5 cm from the centre. Find the length of the chord.CAT 2022 Slot 1 · medium
A chord of length 24 cm is drawn in a circle of radius 13 cm. Find the perpendicular distance from the centre of the circle to the chord (in cm).CAT 2022 Slot 2 · medium

CAT 2021

In a circle of radius 15 cm, two parallel chords of lengths 18 cm and 24 cm lie on the same side of the centre. What is the distance between the…CAT 2021 Slot 1 · medium
Two circles of radii 9 cm and 4 cm touch each other externally. What is the length (in cm) of their direct common tangent?CAT 2021 Slot 2 · easy
In a circle of radius 13 cm, AB is a chord of length 24 cm. CD is a chord of length 10 cm parallel to AB, lying on the opposite side of the centre.…CAT 2021 Slot 3 · medium

CAT 2020

CAT 2019

What is the length (in cm) of another chord of the same circle that is at a distance of 24 cm from the centre?CAT 2019 Slot 1 · medium
In a circle of radius 13 cm, two parallel chords of lengths 24 cm and 10 cm lie on opposite sides of the centre. What is the distance (in cm) between…CAT 2019 Slot 2 · medium

CAT 2018

What is the length of a chord at a distance of 8 cm from the centre?CAT 2018 Slot 1 · easy
What is the length of a chord at a distance of 15 cm from the centre?CAT 2018 Slot 2 · medium

CAT 2017

What is the length (in cm) of a chord of the same circle that is at a distance of 12 cm from the centre?CAT 2017 Slot 2 · medium

CAT 2016