If two chords AB and CD intersect at point E inside a circle, what is the relati

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Question: If two chords AB and CD intersect at point E inside a circle, what is the relationship between the segments AE, EB, CE, and ED?

Options:

Correct Answer: AE * EB = CE * ED

Solution:

According to the intersecting chords theorem, AE * EB = CE * ED.

If two chords AB and CD intersect at point E inside a circle, what is the relationship between the segments AE, EB, CE, and ED?

If two chords AB and CD intersect at point E inside a circle, what is the relationship between the segments AE, EB, CE, and ED?

Step 1: Identify the two chords AB and CD that intersect at point E inside the circle.
Step 2: Label the segments of the chords: AE is the segment from A to E, EB is the segment from E to B, CE is the segment from C to E, and ED is the segment from E to D.
Step 3: Understand that the intersecting chords theorem states that when two chords intersect inside a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.
Step 4: Write down the relationship: AE multiplied by EB equals CE multiplied by ED.
Step 5: Conclude that AE * EB = CE * ED is the relationship between the segments.

Intersecting Chords Theorem – When two chords intersect inside a circle, the products of the lengths of the segments of each chord are equal.