Butterfly Theorem in Euclidean Geometry

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5 Questions

What is the result of (MX/MY)^2 based on the given equations and intersecting chords theorem?

(PM)^2-(MX)^2/(PM)^2-(MY)^2

What does the equation (AX⋅DX)/(CY⋅BY) represent in the context of the intersecting chords theorem?

Ratio of lengths of intersecting chords

How is the ratio (PX⋅QX)/(PY⋅QY) relevant in the context of the given equations and intersecting chords theorem?

Describes the slope of the intersecting chords

What does the expression (PM-XM)⋅(MQ+XM)/(PM+MY)⋅(QM-MY) signify based on the given equations and intersecting chords theorem?

Ratio of vertical distances from the intersection point

In the context of the equations and intersecting chords theorem, what does (MX)^2/(MY)^2 represent?

Ratio of squares of vertical distances

Test your knowledge of the classical Butterfly Theorem in Euclidean geometry, which involves the midpoints of chords and intersecting lines in a circle. This quiz covers the statement of the theorem and its formal proof.

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