Question

*Chords AB and PQ of a circle intersect inside the circle at point M. If AM = 4, BM = 12, PM = 8, find QM.*

1️⃣ 10
2️⃣ 12
3️⃣ 8
4️⃣ 6​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

Chords AB and PQ of a circle intersect inside the circle at point M. If AM = 4, BM = 12, PM = 8, then QM

• 10

• 12

• 8

• 6

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

$\displaystyle \sf{ \implies \: QM = \frac{4 \times 12}{8} }$

$\displaystyle \sf{ \implies \: QM = \frac{48}{8} }$

$\displaystyle \sf{ \implies \: QM = 6 }$

FINAL ANSWER

The length of QM = 6

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