A Treatise On Higher Trigonometry

Cover A Treatise On Higher Trigonometry
A Treatise On Higher Trigonometry
J B John Bascombe Lock
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(21) If 10 = IX, prove that one angle of the triangle ABC is 600.
(22) If two of the angular points and the radius of the cir- cumscribing circle of a triangle are given, the loci of the centre of the nine-point circle and of the ortho-centre are circles.
(23) Prove that a triangle can be constructed whose sides are a cos yl, 6 cos i?, c cos C and that its area is 2 A . Cos A . Cos B . Cos C.
(24) If i^i, ^2 J ^3 ^^® ^^^ Yi\. D. N of the circumscribed circles of BIC, CIA, AIB, prove that B^^ .
...R. / . R^'=R^ . AI. BI . CI.
(25) If the two straight lines which bisect the angles A and C of a triangle ABC, meet the circumference of the circumscribing circle in R and S, then RS is divided by CB, BA into three parts which are in the ratio sin^i^l : 2sin^^ . Sin^i? . Sin^C : sin^lC.
(26) If a point be taken in an equilateral triangle such that its distances from the angular points are proportional to the sides of a triangle ABC, the angles between these distances will be ^ + A, lir+B, ^7r + C.


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