In a circle, if two chords AB and CD intersect at point E, which of the followin

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Question: In a circle, if two chords AB and CD intersect at point E, which of the following is true?

Options:

Correct Answer: AE * EB = CE * ED

Solution:

According to the intersecting chords theorem, the products of the segments of the chords are equal, hence AE * EB = CE * ED.

In a circle, if two chords AB and CD intersect at point E, which of the following is true?

In a circle, if two chords AB and CD intersect at point E, which of the following is true?

Step 1: Identify the two chords AB and CD in the circle.
Step 2: Locate the point E where the two chords intersect.
Step 3: Label the segments of the chords: AE, EB for chord AB and CE, ED for chord CD.
Step 4: Understand the intersecting chords theorem, which states that 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 5: Write the equation based on the theorem: AE * EB = CE * ED.
Step 6: Conclude that this relationship holds true for the intersecting chords in the circle.

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