CDS 2026 (I) Elementary Mathematics, question 73

Topic: Geometry

Answers by SolvedPaper. UPSC has not released the official answer key for this paper yet. We will update it when they do.

Q73

A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.

Question : ABCD is a quadrilateral such that AC bisects ∠A\angle A and ∠C\angle C. Is AB/DCAB/DC equal to AD/BCAD/BC ?

Statement-I : AB is parallel to DC

Statement-II : AD is parallel to BC

Which one of the following is correct in respect of the above Question and the Statements ?

  1. (a) The Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
  2. (b) The Question can be answered by using either Statement alone
  3. (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
  4. (d) The Question can be answered even without using both the StatementsCorrect answer

Solution.

Answer: (d) The Question can be answered even without using both the Statements

  1. Because AC bisects both ∠A\angle A and ∠C\angle C, triangles ABC and ADC have two equal angles and the common included side AC.
  2. They are congruent by ASA.
  3. Consequently AB=ADAB = AD and BC=DCBC = DC, which immediately gives AB/DC=AD/BCAB/DC = AD/BC.