In figure 3.78, chord MN and chord RS intersect at point D. (1) If RD = 15, DS = 4, MD = 8 find DN (2) If RS = 18, MD = 9, DN = 8 find DS

In figure 3.78, chord MN and chord RS intersect at point D.

(1) If RD = 15, DS = 4, MD = 8 find DN

(2) If RS = 18, MD = 9, DN = 8 find DS

Doubtly Asked 24 Oct 2026 Save WhatsApp Report

1 answer

Answer: (1) DN = 7.5 (2) DS = 12 or 6

By the theorem of chords intersecting inside a circle, \(RD \times DS = MD \times DN\).

(1)

\[15 \times 4 = 8 \times DN\] \[DN = \frac{60}{8} = 7.5\]

(2) Let DS = x, then RD = 18 − x.

\[(18 - x)x = 9 \times 8 = 72\] \[x^2 - 18x + 72 = 0\] \[(x - 12)(x - 6) = 0\]

DS = 12 or DS = 6 (both are possible).

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

Was this answer helpful?