CDS 2024 · PYQ · Geometry / Similar Triangles · medium
What is the length of MN? (Two parallel line segments PQ = 5 cm and RS = 3 cm are perpendicular to a horizontal line AB. The point of intersection of PS and QR is M and MN is perpendicular to QS.)
A.3/8 cm
B.5/8 cm
C.9/8 cm
D.15/8 cm✓ Correct
Explanation
Using similar triangles, MN is the harmonic-mean-related quantity: 1/MN = 1/PQ + 1/RS = 1/5 + 1/3 = 8/15, so MN = 15/8 cm. This is a classic result where MN = (PQ × RS)/(PQ + RS) = 15/8 cm.
💡 Practice unlimited CDS PYQs + AI-tracked progress on each topic. Sign up free →
Want more CDS practice?
Free daily 10-Q quiz · adaptive mocks · 4,000+ verified PYQs · AI doubt solver in Hindi + English