...circles touch each other; to compare the area of the triangle formed by joining their centres with the area of the triangle formed by joining the points of contact. 40. If four straight lines intersect each other, and form four triangles; the circles which circumscribe...

...circles touch each other; to compare the area of the triangle formed by joining their centres with the area of the triangle formed by joining the points of contact. Let three equal circles, whose centres are A, B, C, touch each other in D, F, E. Join AB, BC, CA, ED,...

...circles touch each other, to compare the area of the triangle formed by joining their centres with the area of the triangle formed by joining the points of contact Let three equal circles, whose centres are A, B, C, touch each other in D, E, F. Join AB, BC, CA, ED,...

...circles touch each other; to compare the area of the triangle formed by joining their centres with the area of the triangle formed by joining the points of contact. 102. Four equal circles touch each other and a given circle externally : compare the radius of one...

...given side. 101. The area of the triangle formed by joining the centres, may be shewn to be four times the area of the triangle formed by joining the points of contact of the circles. 102. If the radius of the given circle be unity, the radius of each of the four equal...

...given angle, find the locus of their intersection. 10. A, B, C are the angles of a plane triangle, S is the area of the triangle formed by joining the points of contact of the inscribed circle, and S' is the area of the triangle made by joining the intersections of the...

...the parabola. 85. The area of the triangle formed by three tangents to a parabola is equal to half the area of the triangle formed by joining the points of contact. 86. PQ is any chord of a parabola cutting the axis in L ; JR, R' are the two points in the parabola...

...circle. 149. The area of the triangle formed by joining the centers, may be shewn to be four times the area of the triangle formed by joining the points of contact of the circles. 150. Let AB be the base of the given segment, C its middle point. Let DCB be the required...

.../ / "{a0(l — a-0)}*da<f0 .{- / / IT 41T1 — . 3. If the equation of the conic (referred to ABC) be the area of the triangle formed by joining the points of contact is, in parts of the triangle ABC, _ (r+p)(r + q) (q + r) ' O, fj and the centre of this conic is -...

...opposite side 250 feet, find approximately the number of minutes in the other acute angle. 257. Shew that the area of the triangle formed by joining the points of contact of the inscribed circle, or an escribed circle, of a triangle is ^ , -where p is the radius of the...