Previous Year Questions

We are given two intersecting chords MN and PQ in a circle, where the point of intersection is O. We are provided with the following information:

· MO = 9 cm

· ON = 5 cm

· OQ = 6 cm

· We need to find the value of OP.

Step 1: Use the Intersecting Chord Theorem

The Intersecting Chord Theorem states that if two chords intersect at a point inside the 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.

Mathematically, this can be written as:

MO X ON=PO X OQ

Step 2: Substitute the known values

We know:

· MO = 9 cm

· ON = 5 cm

· OQ = 6 cm

Let OP = x (the value we need to find). Using the Intersecting Chord Theorem:

9*5=6*OP

OP=7.5 cm

Step 3: Conclusion

Therefore, the value of OP is 7.5 cm.

The correct answer is a) 7.5.