Pythagorean Pondering

Geometry Level 4

Triangle PQR is right-angled at Q. A full circle is drawn with hypotenuse PR as a diameter. Then semi circles are drawn using the other two sides as a diameter.

This creates 6 regions, whose areas from A0 to A5 have been marked.

Which of the following is a correct relation?

A2 + A3 = A4 + A5 A0 = A2 + A3 A1 = A2 + A3 A0 = A4 + A5

1 solution

Junyi Liu
Dec 30, 2017

This is how I solve it: ① $A_{1}$ $=$ $A_{0}$ $+$ $A_{4}$ $+$ $A_{5}$ ② $A_{1}$ $=$ $A_{2}$ $+$ $A_{3}$ $+$ $A_{4}$ $+$ $A_{5}$ ③ $A_{0}$ $+$ $A_{4}$ $+$ $A_{5}$ $=$ $A_{2}$ $+$ $A_{3}$ $+$ $A_{4}$ $+$ $A_{5}$ ④ $A_{0}$ $=$ $A_{2}$ $+$ $A_{3}$

Pythagorean Pondering

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