GATE 2024 AR — Planning – Question 10

Correct answer: (A) A rhombus

Explanation

Picture the double cone: two identical right circular cones glued base to base, with their axis vertical. The two vertices are at the top and the bottom.

**A plane through both vertices** contains the common axis. Such a plane cuts the double cone along a plane through its axis, so it passes through the diameter of the common base.

• The section of the upper cone is an **isosceles triangle** whose base is that diameter and whose other two sides are slant lines of the cone.
• The section of the lower cone is an identical isosceles triangle pointing downward on the same base.

Together the two triangles form a four-sided figure. All four sides are slant heights of the same cones, so **all four sides are equal**. A quadrilateral with four equal sides is a **rhombus** (option A).