Professor Layton and the Curious Village

Puzzle 011: Arc and Line

Original diagram for Puzzle 011: Arc and Line

A rectangle sits inside a quarter circle with one corner at the centre, so how long is its diagonal?

Chapter
Chapter 1
Location
Manor Parlor · Simon
Picarats
20 picarats
Type
Write Answer
Region
Same in all versions
Hint 1: A gentle nudge. Tap to flip.
Hint 1

You could reach for Pythagoras here, but you don't have to. Look for a shortcut in the shape itself.

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Hint 2: The key idea. Unlocks after the previous card is flipped.
Hint 2

A rectangle has two diagonals. What do you know about their lengths?

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Hint 3: Almost there. Unlocks after the previous card is flipped.
Hint 3

Follow the other diagonal from B to D. Where does it start, and where does it end?

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Answer: See the answer. Unlocks after the previous card is flipped.
Answer

The answer is 10.

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Solution, FAQ and sources

Solution

1. In any rectangle the two diagonals are the same length, so AC = BD. 2. B is the centre of the circle and D lies on the arc, so BD is a radius. 3. The marked lengths along the radius on the diagram add up to 10.

So AC = BD = radius = **10**. No calculation with the sides of the rectangle is needed.

About this puzzle

A quarter of a circle is drawn with its centre at point B. A rectangle ABCD sits inside it, with corner B at the centre and the opposite corner D touching the curved edge. The lengths marked on the diagram tell you the size of the circle. How long is the rectangle’s diagonal AC?

Unofficial fan guide, not affiliated with LEVEL-5. Puzzle description, hints and solution written by Hint by Hint.

Similar puzzles: Puzzle 013: Sinking Ship, Puzzle 008: Farm Work, Puzzle 016: Triangles and Ink, Puzzle 009: One Poor Pooch

All Professor Layton and the Curious Village puzzles

FAQ

What is the answer to Puzzle 011, Arc and Line, in Professor Layton and the Curious Village?

The answer is 10.

Where do you find Puzzle 011 in Curious Village?

Puzzle 011 appears in Chapter 1, in the Manor Parlor area, when you talk to Simon.

How many picarats is Curious Village Puzzle 011 worth?

20 picarats.

Sources

Facts checked on November 14, 2026

Unofficial fan guide. Not affiliated with, endorsed by, or sponsored by LEVEL-5 Inc. Professor Layton, The New World of Steam, and all related names, characters, and trademarks are the property of their respective owners.