SSC CGL 2024 Tier-I · 11 September 2024, Shift 1 · Quantitative Aptitude · Question 11 of 95

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 10 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

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

(a)6.5
(b)6
(c)7
(d)7.5

Answer

Why

Correct — D. Two chords crossing inside a circle cut each other into pieces whose products are equal.

Intersecting-chords rule: MO × ON = PO × OQ
9 × 5 = OP × 6
45 = 6 × OP
OP = 45 ⁄ 6 = 7.5 cm → option (d)

The radius and the full lengths of MN and PQ are never needed — the rule uses only the four segments meeting at O.

Why the others are wrong

(a)
6.5 — 6.5 gives 6 × 6.5 = 39 on the right, against MO × ON = 45 on the left. The two products have to match exactly.
(b)
6 — 6 simply repeats the given OQ. It would need MO × ON to be 36, and 9 × 5 is 45.
(c)
7 — 7 gives 6 × 7 = 42, three short of 45. The equation is exact, so the fractional 7.5 is the true value and not a rounding artefact.

Concept

When two chords of a circle cross at an interior point O, the products of their segments are equal: MO × ON = PO × OQ.

It comes from similar triangles. Angles PMO and OQN stand on the same arc PN and are equal, and the angles at O are vertically opposite, so triangle MOP is similar to triangle QON — which gives MO ⁄ QO = PO ⁄ NO.

That common product is the power of the point O. It is the same number for every chord drawn through O, which is why one pair of segments settles the other.

O here is only the crossing point of the two chords, not the centre of the circle. Nothing in the question says the chords pass through the centre, and nothing needs it to.

Key facts

Intersecting chords: MO × ON = PO × OQ for any two chords meeting at an interior point O.
The rule follows from triangle MOP being similar to triangle QON.
Here MO × ON = 45, so every chord through O splits into two pieces multiplying to 45.
OP = 45 ⁄ 6 = 7.5 cm, and OP need not be a whole number.

Study next

Tangent–secant rule: PT² = PA × PB from an external pointPower of a point for a point outside the circleAngles in the same segment and the cyclic quadrilateral results that follow

Common traps

Pairing segments of the same chord, writing MO × PO = ON × OQ.
Assuming an SSC length must be a whole number and rounding 7.5 down to 7.
Treating O as the centre and reaching for the radius.

The same circle chapter is asked through the chord–distance–radius right triangle at 18 Sep 2024, 09:00, Quant Q.25 and 19 Sep 2024, 12:30, Quant Q.16.

Decide which relation the question has handed you — segments of two crossing chords, or a perpendicular dropped from the centre — before writing anything down.

Related PYQs

No directly related past PYQ was found.