SSC CGL 2024 Tier-I · 23 September 2024, Shift 2 · Quantitative Aptitude · Question 2 of 100

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.

XAB and XCD are two secants to a circle. If XA = 18 cm, AB = 22 cm and XC = 24 cm, then find the value of XD (in cm).

(a)28
(b)34
(c)30
(d)21

Answer

Why

Correct — C. Rule: for two secants drawn from an external point X, XA × XB = XC × XD — the power of the point X.

Both products run from X to the far intersection, so XB is the whole secant, not the segment AB.

XB = XA + AB = 18 + 22 = 40 cm
XA × XB = 18 × 40 = 720
720 = XC × XD = 24 × XD

XD = 720 ⁄ 24 = 30 cm → option (c)

Why the others are wrong

(a)
28 — 28 is XC + AB − XA = 24 + 22 − 18, an addition shortcut with no bearing on the theorem. Test it: 24 × 28 = 672, not the 720 that XA × XB fixes.
(b)
34 — 34 fails the product test — 24 × 34 = 816 against the required 720. It sits close enough to 30 to survive a glance, which is exactly why the multiplication is worth ten seconds.
(d)
21 — 21 is less than XC = 24, so D would fall between X and C. Impossible when C is named as the near intersection and D as the far one, and 24 × 21 = 504 misses 720 anyway.

Concept

The power of a point is one theorem in three costumes, and this is the two-secant costume.

From an external point X, every line cut by the circle gives the same product of the two distances to the circle. Two secants therefore satisfy XA × XB = XC × XD, and if one line is a tangent XT, the same quantity is XT².

The distances are always measured from X, never between the intersection points. That single reading decides the question: the given AB is a gap inside the circle, and it has to be added to XA before it can be used.

The naming convention does the work. In 'XAB', A comes before B, so A is nearer to X — and the same for C before D in 'XCD'.

Key facts

For two secants from an external point, XA × XB = XC × XD, with B and D the far intersections.
The tangent form of the same theorem is XT² = XA × XB.
On any one secant the far distance exceeds the near distance, so XD is always greater than XC.
Here XA × XB = 18 × 40 = 720, giving XD = 720 ÷ 24 = 30 cm.

Study next

The tangent–secant form XT² = XA × XB and the length of a tangent from an external pointTwo chords meeting inside a circle, where PA × PB = PC × PDRecovering the radius from a secant and the distance of the external point from the centre

Common traps

Using AB, the chord, where the theorem wants XB, the whole secant
Treating XC as the far intersection when the lettering makes it the near one
Reporting 720, the power of the point, instead of dividing it by XC

SSC dresses this theorem as two secants, as a tangent with a secant, or with the distance from the centre supplied so the radius can be recovered.

Also asked 19 Sep 2024, 09:00, Quant Q.15 and 26 Sep 2024, 16:00, Quant Q.25, both of which give the distance from the centre and ask for the radius.

Related PYQs

No directly related past PYQ was found.