...BE is a diameter, for then ifBAE is r't; therefore in any triangle the product of two sides equals the product of the diameter of the circumscribed circle by the altitude upon the third side. Ex. 296. To find the bisectors of the angles of a triangle, given the sides. tc= - "[abs(s — c)]l....

...altitude, BE is a diameter, for then ^BAE is r't; therefore in any triangle the product of two sides equals the product of the diameter of the circumscribed circle by the altitude upon the third side. Ex. 296. To find the bisectors of the angles of a triangle, given the sides. t c = - r [abs(s — c)]*....

...r'. IV. Solution by Irma Luelleman, Mattoon, Itts. In any triangle the product of two sides equals the product of the diameter of the circumscribed circle by the altitude upon the third side. If the triangles are ABC and AB'C and h is the altitude from C to the line AB' then in AABC we have...

...PROOF OF GEOMETRICAL THEOREM. By TAKESHI O.MACHI, In Sendai, Japan. Another proof of the theorem that in any triangle, the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector....

...OF GEOMETRICAL THEOREM. By TAKESHI OMACHI, In Sendai, Japan. • Another proof of the theorem that in any triangle, the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector....

...joining their homologous vertices are concurrent. What happens when the triangles are equal ? 510. In any triangle the product of two sides is equal to the square of the bisector of the included angle plus the product of the segments into which it divides...

...EXERCISES 668 If PA = 3, AB = 9, find PT. 669 If PT = 8, PB = 16, find PA. PROPOSITION XXXIII. THEOREM 381 In any triangle, the product of two sides is equal to the square of the bisector of their included angle, increased by the product of the segments of the third...

...ZA=^D (?) (250). .-. these A are similar (?). .-. e: d=h:a(?) (323, 3). QED 1(;2 163 338. THEOREM. In any triangle the product of two sides is equal to the square of the bisector of their included angle, plus the product of the segments of the third side...

...EXERCISES 668 If PA = 3, AB = 9, find PT. 669 If PT = 8, PB = 16, find PA. PROPOSITION XXXIII. THEOREM 381 In any triangle, the product of two sides is equal to the square of the bisector of their included angle, increased by the product of the segments of the third...

...35 39. From a figure like Fig. 35, but with k+x passing through the center of the circle, prove that in any triangle the product of two sides is equal to the diameter of the circumscribed circle multiplied by the altitude upon the third side. 40. Find the length...