...provided n be less than m. 80. The product of all the lines that can be drawn from one of the angles of a regular polygon of n sides inscribed in a circle whose radius is a, to all the other angular points, is na"~ l . 81. If the exterior angles of a quadrilateral figure...

...of the expansion of (a+b)n2. The product of all the lines, that can be drawn from one of the angles of a regular polygon of n sides, inscribed in a circle whose radius is a, to all the other angular points = no. "~1» 3. If the sun's longitude = c, and the obliquity of...

...FTF + f.- — 1. Aa DO Cc 17. The product of all the lines that, can be drawn from one of the angles of a regular polygon of n sides, inscribed in a circle whose radius is a, to all the other angular points = nan~l. 18. Extract the square root of cos 4A ± V — 1 sin 4A....

.... 2 2 2 ' nA nB nC or = — 1 ± 4 cos — cos — cos — , according as n is odd or even. (22) In a regular polygon of n sides inscribed in a circle •whose radius is (r), if a be the distance of any point from the centre, and perpendiculars be drawn from this point upon...

...sin — to n sin — . 2i L 4. The product of all the lines that can be drawn from one of the angles of a regular polygon of n sides inscribed in a circle whose radius is a to all the other angular points is na"~l. 5. If P>, p,, •..p„-tt Pv, t>e tne perpendiculars drawn...

...triangle = r, (*— a) ; (2) area of triangle = ./s(s— a) (s—b) (s — c) ; 56 EXAMINATION PAPERS. 4. Find the perimeter of a regular polygon of n sides inscribed in a circle of radius r. Shew that the area of the rectangle contained by two lines equal to the sides of the squares...

...interior angle : express each in circular measure, and find the number of sides of the polygon. 11. The perimeter of a regular polygon of n sides, inscribed in a circle of radius r, is 2nr sin - . n 12. The perimeter of a regular polygon of n sides, described about a...

...inscribed circle, (2) the circumscribed circle of a regular hexagon whose side is a. 4. Show that the side of a regular polygon of n sides, inscribed in a circle whose radins is R, is 5. Show by Euclid IV. 10, that the side of a regular decagon. inscribed in a circle...

...indefinitely increases, the apothem towards the radius as its limit. Given : AB, a side, and OP, the apothem, of a regular polygon of n sides inscribed in a circle whose radius is OA ; To Prove : As n increases, OP increases towards OA as limit. Since OP is _L to AB, (377) OP'**OA*—A?....

...Prove (a) if Л +В+С=я, tan 4+tan B+t&n С =ta,nA tan B tan ('. (6) J(a+6)coeC=a+6+c. 4. (a) If p be the perimeter of a regular polygon of n sides inscribed in a circle, and P be the perimeter of the corresponding polygon circumscribing the circle ; and also if plt P!...