In a circle, two chords MN and PQ intersect at O. If MO = 9 cm, ON = 5 cm and OQ = 6 cm, then find the length of OP (in cm).

Question

Accepted Answer

When two chords MN and PQ intersect at point O inside a circle, the products of the segments of each chord are equal. This is known as the intersecting chords theorem.

Given:
MO = 9 cm, ON = 5 cm, OQ = 6 cm

According to the theorem:
MO × ON = PO × OQ

Let OP = x cm.

So, 9 × 5 = x × 6
45 = 6x
x = 45 / 6 = 7.5 cm

Therefore, the length of OP is 7.5 cm.

Answer

Answer

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