Oxford University Maths Admissions Test 2023 Question 3

University of Oxford Mathematician Dr Tom Crawford answers each Oxford Maths Admissions Test question in under 60 seconds. This is Q3 from the 2023 MAT.

You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.

[michaelcolbourn]

To get the first and last component I just used Pythagoras again instead of trig.

(r1)² + (r1)² = (c1)²
2(r1)² = (c1)²
√2 × r1 = c1

So √2 × r2 = c2 by symmetry

So (√2 × r1) + r1 + r2 + (√2 × r2) = √2

√2(r1 + r2) + r1 + r2 = √2

(r1 + r2)(√2 + 1) = √2

r1 + r2 = √2 / (√2 + 1)

r1 + r2 = √2 (√2 - 1)

r1 + r2 = 2 - √2

[johnmaynard]

This is informative and enjoyable, a test has never looked more fun 😎👍

[zzzluvsk]

Two two root two root two root two got it 💪

[josepereira]

So the information “the area of the larger is 10x the area of the smaller circle” is useless?

[Blud]

How do you call it r1 and the other r2 while they are larger than the actual radii of those circles?

[sjrhrhcytjigsjrhrhcytjig]

Sir, can u make ur self more small to see full the exam

[drake]

So is that bit about the areas just a distraction? Because i cant find a way to solve it using those areas.

[alexanderojo]

How do you know that from point B to the horizontal radius is also equal to r1?

[harrythompson]

These are 10th standard questions in India, maybe we should've gone to college after that...