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If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the...
Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ... - Page 69
by Euclid - 1845 - 199 pages

## Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - Mathematics - 1889 - 356 pages
...the angle A. Show that the construction is impossible unless 2C + A is less than a right angle. 7. If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles which this line makes with the line touching the circle shall be equal...

## Practical Plane and Solid Geometry, Including Graphic Arithmetic

Isaac Hammond Morris - Geometry, Plane - 1890 - 440 pages
...the point of contact is perpendicular to the line touching the circle.' Also the converse of this. ' If a straight line touch a circle, and from the point...line, the centre of the circle shall be in that line.' (Eue. in. 18 and 19.) 3. There is a large variety of problems of this kind, and in cases of difficulty...

## Practical Plane Geometry: Giving the Simplest Modes of Constructing Figures ...

John Fry Heather - Geometry, Modern - 1890 - 252 pages
...Angles in the same segment of a circle are equal to one another. (Eu. III., 21.) 137. THEOR. 23. — If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles which this line makes with the line touching the circle shall be equal...

## The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...given point a chord of a given circle which bisected by a given straight line. PROPOSITION 32. THEOREM. If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by this line with the line touching the circle shall be equal to...

## Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - Education - 1890 - 526 pages
...and enunciation of tlioae propositions of Euc. Bk. III., in which this definition is made use of. 3. If a straight line touch a circle, and from the point of contact a straight line lie drawn cutting the circle, the angles which this line makes with the line touching the circle shall...

## Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - Geometry - 1890 - 442 pages
...As, v ABQP is a cyclic quad. A And it has been shown that PAB < rt. A . Proposition 32. THEOREM — If a straight line touch a circle, and from the point of contact a straight line is drawn dividing the circle into two segments, the angles made by this line with tlie tangent are...

## Annual Report of the Chief Superintendent of Education

1891 - 718 pages
...whether that angle be right, obtuse, or acute. (6) Prove the case in which the angle is obtuse. 3. (a) If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by this line with the line touching the circle must be equal to...

## Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - Education - 1892 - 508 pages
...straight line which joins their centres, being produced, shall pass through tho point of contact. 3. If a straight line touch a circle, and from the point of 8 contact a chord be drawn, the angles which this chord makes with the tangent shall be equal to the...