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Arc and Line is a puzzle in Professor Layton and the Curious Village.

Puzzle

US Version

As shown in the diagram below, you have one-fourth of a circle. Within this circle is rectangle ABCD, which touches the edge of the circle at point D.

Assuming that point B is located at the center of the circle, how long is diagonal line AC?

UK Version

As shown in the diagram below, you have a quarter of a circle. Within this circle is rectangle ABCD, which touches the edge of the circle at point D.

Assuming that point B is located at the centre of the circle, how long is diagonal line AC?

Hints




Click a Tab to reveal the Hint.

Surely somebody must have looked at the diagram and realized that the triangle formed by points A, B, and C is a right triangle.

That's sharp thinking and exactly right. However, are you sure there isn't a much easier way to find the answer?

You don't need the Pythagorean theorem to answer this one. Something else in the diagram should be the exact same length as AC.

Notice that diagonal line AC within the rectangle is the same size as the diagonal line BD.

Have you also noticed that BD is also the same length as another part of this diagram?


Solution

Incorrect

No, no, no!

Look at things again. You shouldn't have to do any difficult calculations to get to the answer.

Correct

US Version

Righto!

Diagonal line AC is exactly the same length as diagonal line BD. BD is the same length as the radius of the circle, so once you've figured that out, the only thing left to do is add five and five.

UK Version

That's right!

Diagonal line AC is exactly the same length as diagonal line BD. BD is the same length as the radius of the circle, so once you've worked that out, the only thing left to do is add five and five.

CV011S

A big thanks to http://professorlaytonwalkthrough.blogspot.com