The GATE Grind

GATE 2026 XH2 (English) – Question 12

Reasoning and Comprehension · Quantitative reasoning · 1 mark · Multiple choice

Let $\triangle ABC$ be an isosceles triangle with the base $AB$ of length 8 units. Let $CD$ be a perpendicular of length 4 units drawn from the vertex $C$ onto the base $AB$ and $AC = BC$.

Then, which of the following is the set of values of the angles (in degrees) $CAB$, $ABC$, $BCA$ respectively?

  1. 45, 45, 90
  2. 100, 40, 40
  3. 90, 45, 45
  4. 40, 40, 100

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) 45, 45, 90

Explanation

Because $AC = BC$, the perpendicular from $C$ meets $AB$ at its midpoint $D$, so $AD = DB = 4$. Then $CD = AD = 4$, so triangle $ADC$ is a right isosceles triangle and $\angle CAB = 45^\circ$. By symmetry $\angle ABC = 45^\circ$, and $\angle BCA = 180^\circ - 90^\circ = 90^\circ$.