*Chords AB and PQ of a circle intersect inside the circle at point M. If AM = 4, BM = 12, PM = 8, find QM.
Answers
SOLUTION
GIVEN
- Chords AB and PQ of a circle intersect inside the circle at point M.
- If AM = 4, BM = 12, PM = 8
TO DETERMINE
The length of QM
EVALUATION
Here it is given that Chords AB and PQ of a circle intersect inside the circle at point M
We know that if two chords of a circle intersect inside a circle, the product of the lengths of the segments of first chord at the point of intersection is equal to the product of the lengths of segments of the second chord
Here it is also stated that
AM = 4, BM = 12, PM = 8
Since the Chords AB and PQ of a circle intersect inside the circle at point M
AM × BM = PM × QM
∴ 4 × 12 = 8 × QM
FINAL ANSWER
The length of QM = 6
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