Mathematics in Ancient and Medieval India c6.s10.13

c6.s10.13

Now two triangles viz. COD ( Fig. 16 ) with sides a₁( a₂, b₂, c₂ ) and AOD with sides a₂ (a₁, b₁, c₁) are made and joined with their common side OD (=a₁ a₂). On the other side of AC two triangles viz. AOB with sides b₁ (a₂, b₂, c₂) and BOC with sides b₂ (a₁, b₁, c₁) are made and joined with their common side OB = b₁ b₂. This gives a quadrilateral ABCD with sides b₁ c₂, b₂ c₁, a₁ c₂, a₂ c₁, in order. The diagonals of a quadrilateral are at right angles. From (e), p. 53, the circumradius of the triangle ABC = (b₂ c₁ × b₁ c₂)/(2b₂ b₁) = (c₁ c₂)/2.