# Exercises on the Geometry and Measurement of Plane Figures, Being Solutions of the Theorems, Problems and Questions in 'Wormell's Modern Geometry'

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## Description

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1883 edition. Excerpt: ... Construct a circumference such that A B shall be a chord and shall cut off a segment, the angle of which shall be equal to the angle C. From A draw A F perpendicular to A B and equal to the given height. Through F draw F E parallel to A B and meeting the circumference in C. A C B is the triangle required. 5th. Let A B, Z C, and the height A D be given. Make an angle A C B = the given angle, and find in the side C A a point, A, such that its distance from C B = the given height (as in Problem 5). From A, with radius A B, describe an arc cutting C B in B, then A B C is the triangle required. 52. Construct a triangle, having given the radius of the inscribed circle, one angle, and the height taken from it. Analysis.--Suppose the problem solved, and let A B C be the triangle. Let A G be the height from A, and let O be the centre of the inscribed circle, and OD, OE, the perpendiculars from O on the sides; then AO bisects the angle A O E = the given radius, and B C is a tangent to the inscribed circle and also a tangent to the circle described with A as centre and A G as radius. Synthesis.--Make an zCAB = the given angle, and bisect it in AO. Take a point, O in AO, such that its distance, OE, from AC = the given radius, and describe a circle with O as centre and O E as radius. Also, with A as centre and the given height as radius, describe another circle. Draw B C a common tangent to these two circles; then ABC will be the circle required. 53. Describe with given radii two circles which shall touch each other and two straight lines which intersect. Let A B, A C be the straight lines. Let M N be a straight line parallel to A B at a distance equal to the first radius, and, M R a straight line parallel to A C at a distance equal to the B..".show more

## Product details

- Paperback | 30 pages
- 189 x 246 x 2mm | 73g
- 13 Sep 2013
- Rarebooksclub.com
- United States
- English
- black & white illustrations
- 1236944364
- 9781236944368