SSC CGL 2025 Tier-I · 16 September 2025, Shift 1 · Quantitative Aptitude · Question 21 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 13 September 2026.

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A right triangle ABC is inscribed in a circle with a diameter of 10 cm. An altitude BD is drawn from the vertex B to the hypotenuse AC. If the length of the leg AB is 6 cm, what is the length of the segment AD?

(a)3.6 cm
(b)4 cm
(c)4.8 cm
(d)6 cm

Answer

Why

Correct — A. A right angle inscribed in a circle stands on a diameter, so the hypotenuse is 10 cm.

AC = diameter = 10 cm, right angle at B, AB = 6 cm
Triangles ADB and ABC are similar (shared ∠A, right angles at D and B)
So AD⁄AB = AB⁄AC

AD = AB² ÷ AC = 36 ÷ 10 = 3.6 cm → option (a)

Why the others are wrong

(b)
4 cm — 4 cm is 10 − 6, the leg AB subtracted from the hypotenuse. AB is a slanted side, not a piece of AC; the pieces of AC are AD = 3.6 and DC = 6.4.
(c)
4.8 cm — 4.8 cm is the altitude BD, not AD: BD = AB × BC ÷ AC = 6 × 8 ÷ 10 = 4.8. The question asks for AD, the part of the hypotenuse between A and D.
(d)
6 cm — 6 cm is the leg AB itself. In right triangle ADB the hypotenuse is AB, so AD must be shorter than 6 cm.

Concept

Two facts combine. An inscribed angle is half the central angle on the same arc, so a 90° angle at B stands on a 180° arc: AC is a diameter.

The altitude to the hypotenuse splits the triangle into two triangles similar to the whole, giving AB² = AD × AC, BC² = DC × AC and BD² = AD × DC.

The full 6-8-10 triangle.
BC = √(10² − 6²) = 8 cm
DC = 8² ÷ 10 = 6.4 cm (3.6 + 6.4 = 10)
BD = √(3.6 × 6.4) = √23.04 = 4.8 cm

Key facts

A right triangle inscribed in a circle has its hypotenuse as a diameter.
With altitude BD to hypotenuse AC: AB² = AD × AC and BC² = DC × AC.
The altitude satisfies BD² = AD × DC, and BD = AB × BC ÷ AC.

Study next

Altitude to the hypotenuse from the two legsCircumradius of a right triangle as half the hypotenuseMean-proportional relations in a right triangle

Common traps

Answering 4.8 cm, the altitude BD, when the question asks for the segment AD.
Pairing AD with the wrong leg: BC² ÷ AC = 6.4 cm is DC, the piece next to C.

The same 6-8-10 triangle with altitude BD to the hypotenuse returns 21 Sep 2025, 16:00, Quant Q.25, which asks for the altitude: BD = 6 × 8 ÷ 10 = 4.8 cm.

Related PYQs

No directly related past PYQ was found.

Topic: Circle and its chords, tangents, angles subtended by chords of a circle, common tangents to two or more circles — all 140 SSC CGL questions on it, every solved shift.