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463. Given the perimeters of a regular inscribed and a similar circ scribed polygon, to compute the perimeters of the regular inscribed circumscribed polygons of double the number of sides.

464. To draw a tangent to a given circle such that the segment in cepted between the point of contact and a given straight line shall h a given length.

465. To draw a straight line equidistant from three given points.

466. To inscribe a straight line of given length between two gi circumferences and parallel to a given straight line. (See Ex. 137.) 467. To draw through a given point a straight line so that its tances from two other given points shall be in a given ratio (m : n). HINT. Divide the line joining the two other points in the given ra 468. Construct a square equivalent to the sum of a given tria and a given parallelogram.

469. Construct a rectangle having the difference of its base altitude equal to a given line, and its area equivalent to the sum given triangle and a given pentagon.

470. Construct a pentagon similar to a given pentagon and equ lent to a given trapezoid.

471. To find a point whose distances from three given straight 1 shall be as the numbers m, n, and p. (See Ex. 461.)

472. Given two circles intersecting at the point A. To draw thro A a secant BAC such that AB shall be to AC in a given ratio (m: n HINT. Divide the line of centres in the given ratio.

473. To construct a triangle, given its angles and its area.

474. To construct an equilateral triangle having a given area. 475. To divide a given triangle into two equal parts by a line dra parallel to one of the sides.

476. Given three points A, B, C. To find a fourth point Psuch the areas of the triangles APB APC, BPC, shall be equal.

477. To construct a triangle, given its base, the ratio of the o sides, and the angle included by them.

478. To divide a given circle into any number of equivalent part concentric circumferences.

479. In a given equilateral triangle, to inscribe three equal ci

tangent to each other and to the sides of the triangle

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