A.M. ≥ G.M. in a semicircleअर्धवृत्त में A.M. ≥ G.M.A.M. ≥ G.M. in a semicircle

Section 8.5 · Class 11 Maths Ch 8 · interactive diagram

Parts and what they mean

• Length a (लंबाई a) — Here a = 9.
• Length b (लंबाई b) — Here b = 4. Diameter = a + b = 13.
• Radius = A.M. (त्रिज्या = A.M.) — Radius = (a + b)/2 = 6.5, the arithmetic mean.
• Half-chord = G.M. (अर्ध-जीवा = G.M.) — By similar triangles its square is a·b, so it equals √(ab) = 6, the geometric mean.
• A ≥ G always (हमेशा A ≥ G) — A half-chord can never be longer than the radius. Equal only when a = b.

Original diagram drawn by Simple Learning Hub for NCERT Class 11 Maths Ch 8. Report a mistake