...ZA = ZD (?) (250). .'. these A are similar (?). ... c: d= A:a(?) (323, 3). QED 162 163 338. 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...

...and a chord drawn from the point of contact is measured by half the intercepted arc. 3. Demonstrate : In any triangle the product of two sides is equal...circumscribed circle by the altitude upon the third side. 4. Demonstrate: If ABC is a right triangle, C the vertex of the right angle, BD a line cutting AC in...

...product of the segments of the third side formed by the bisector. 8. In any triangle the product of any two sides is equal to the product of the diameter...circumscribed circle by the altitude upon the third side. 9. If through vertex C of triangle ABC a line CE is drawn parallel to AB, and F, the midpoint of AB,...

...CA x BC=CP 2 +APxPB. Ax. 9 .-. ~CP 2 =CAx BC — APxPB, by Ax. 2. QED PROPOSITION XXIV. THEOREM 305. In any triangle the product of two sides is equal...circumscribed circle by the altitude upon the third side. Given the triangle ABC with CP the altitude, ADBC the circle circumscribed about the triangle ABC,...

...• * '3 T , ?/ j. ^ By the theorem, z 2 = ab — xi/ = 15—8 T ' T = 6J> £ V105 = 2.5 +. THEOREM. In any triangle the product of two sides is equal...circumscribed circle by the altitude upon the third side. This enables us, after the Pythagorean Theorem has been studied, to compute the length of the diameter...

...What is the locus of the centres of these circles? Prove the correctness of your answer. 4. Prove that in any triangle the product of two sides is equal...of the diameter of the circumscribed circle by the perpendicular let fall upon the third side from the vertex of the opposite angle. 6. Prove that if...

...grope in the dark in making the selection. Consider the theorem, "In any triangle the product of any two sides is equal to the product of the diameter...circumscribed circle by the altitude upon the third side." We are to prove the product of two lines equal to the product of two others, and this equality suggests...

...PROOF 1. . Prove that a : t = t+ m:C. 2. Then ac = t" + tm = P + rs. 8. . •. Z2 = ac — rs. Ex. 798. In any triangle the product of two sides is equal to the product of the altitude upon the third side and the diameter of the circumscribed circle. HIST. Prove A ABO ~ A EBC....

...median mc upon any side of a triangle, as c, may be derived, namely, PROPOSITION XXIII. THEOREM 425. In any triangle the product of two sides is equal to the square of the bisector of the included angle, increased by the product of the segments of the third...

...median m,. upon any side of a triangle, as c, may be derived, namely, PROPOSITION XXIII. THEOREM 425. In any triangle the product of two sides is equal to the square of the bisector of the included angle, increased by the product of the segments of the third...