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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

To avoid fine, this book should be returned on or before the date last stamped below

10-6-40

JUL 1

1963

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