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Subjects · Leaving Cert Design & Communication Graphics (DCG)

Leaving Cert Design & Communication Graphics (DCG): Tangency: circles & arcs

How often Tangency: circles & arcs comes up on the Design & Communication Graphics papers, every year it was asked, and questions to try.

OL Asked on 5 of the last 9 Ordinary Level papers, most recently in 2025.

Tangency: circles & arcs, Ordinary Level(6 marks)

Quick ones on Tangency: circles & arcs.

(a)A tangent to a circle meets the radius at the point of contact at what angle?
  1. 45 degrees
  2. 90 degrees
  3. 60 degrees
(b)A circle must pass through points A and B. Its centre lies on which line?
  1. A line parallel to AB through A
  2. The line AB itself, extended
  3. The perpendicular bisector of AB
(c)Two circles touch on the outside. How far apart are their centres?
  1. The sum of the two radii
  2. The larger radius only
  3. The difference of the two radii
Show the answers

(a) 90 degrees

(b) The perpendicular bisector of AB

(c) The sum of the two radii

Your turn: Ordinary Level questions on Tangency: circles & arcs.

Ordinary Level

Asked on 5 of the last 9 Ordinary Level papers, most recently in 2025.

Every paper, year by year

YearWhere it came up
2025A4
2024A4
2023Not asked
2022Not asked
2021A2
2019A4
2018A1
2017Not asked
2016Not asked

Links open the State Examinations Commission’s paper for that year.

More Tangency: circles & arcs questions

Tangency: circles & arcs, 3 marks

Two circles touch each other externally. How many common tangents can be drawn to both?

  1. Two
  2. Four
  3. Three
Show the answer

Three

There are two outer tangents plus one through the point of contact, square to the line of centres. Separate circles have four.

Tangency: circles & arcs, 3 marks

An arc blends smoothly into a line or another arc. What must be true at the joining point?

  1. They cross at 90 degrees at that point
  2. They share the same tangent there
  3. They have the same radius there
Show the answer

They share the same tangent there

A smooth join has no kink: both curves head the same way, so they have a common tangent at the point of contact.

Tangency: circles & arcs, 3 marks

A 50 mm arc must enclose a circle of radius 15 mm and touch a circle of radius 10 mm outside. Which locus radii?

  1. 35 mm and 60 mm
  2. 65 mm and 40 mm
  3. 35 mm and 40 mm
Show the answer

35 mm and 60 mm

Enclosing is internal contact, so subtract: 50 - 15 = 35. Outside contact, so add: 50 + 10 = 60. Arcs of these radii cross at the centre.

Other Design & Communication Graphics (DCG) topics

All of Leaving Cert Design & Communication Graphics (DCG)