Intersecting Chords Theorem

Front

What is the Intersecting Chords Theorem?

Back

The Intersecting Chords Theorem states that if two chords intersect inside a circle, the products of the lengths of the segments of each chord are equal.

Front

What is the formula derived from the Intersecting Chords Theorem?

Back

The formula is a × b = c × d, where a and b are the lengths of the segments of one chord, and c and d are the lengths of the segments of the other chord.

Front

What do the angles θ and φ represent in the context of the Intersecting Chords Theorem?

Back

The angles θ are vertically opposite angles, and the angles φ are inscribed angles, which are the same in similar triangles formed by the intersecting chords.

Front

Why do the triangles formed by intersecting chords have proportional lengths?

Back

The triangles have the same angles, which means they are similar triangles, leading to proportional lengths.

Front

What happens if you measure the lengths of the segments of intersecting chords?

Back

If measured accurately, the products of the lengths of the segments will be equal, demonstrating the theorem.

Front

What is an example calculation using the Intersecting Chords Theorem?

Back

For example, if one chord has segments of lengths 71 and 104, and the other has segments of lengths 50 and 148, the products are 71 × 104 = 7384 and 50 × 148 = 7400, which are very close.