Question

A red dot is connected with two non-elastic strings P and Q of equal length. The strings are fixed at points 1 and 2, as shown below. Consider both the strings, points 1, 2, and the red dot are all on the same plane throughout the operations. If one of the strings is fully stretched (taut) at all times, what will be the shape of the path traced by the dot?

• A. Fig A
• B. Fig B
• C. Fig C
• D. Fig D

Hint:

The boundary of the intersection of two circles always has sharp corners at the points of intersection. Any smooth curve option (like an ellipse) can be eliminated instantly.

Answer 1

The Correct Option is D

Step 1: Analyse each taut string.
When string P is taut the dot traces an arc of radius $P$ about point 1; when Q is taut it arcs about point 2.
Step 2: Combine the arcs.
The full path is two joined circular-arc segments.
\[ \boxed{\text{Option 4 (Fig D)}} \]