This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1908 Excerpt: ...circle orthogonally is a straight line. Ex. 359. Show that, if AB is a diameter of a circle which cuts two given circles orthogonally, the polars of A with respect to the two circles intersect in B. Ex. 360. O is a common point of two orthogonal circles, A, A' are the points of contact of one common tangent, B, B' of ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1908 Excerpt: ...circle orthogonally is a straight line. Ex. 359. Show that, if AB is a diameter of a circle which cuts two given circles orthogonally, the polars of A with respect to the two circles intersect in B. Ex. 360. O is a common point of two orthogonal circles, A, A' are the points of contact of one common tangent, B, B' of the other. Show that one of the angles AOA', BOB' is half a right angle and that their sum is two right angles. Ex. 361. Two fixed circles intersect in A, B; P is a variable point on one of them; PA meets the other circle in X and PB meets it in Y. Prove that BX and AY intersect on a fixed circle. Ex. 362. Find the locus of the points at which two given circles subtend the same angle. MISCELLANEOUS PROPERTIES OF THE CIRCLE 85 Ex. 363. If A, B be two fixed points in a fixed plane, and P a point which moves in the plane so that AP=m. BP, where ml, show that P describes a circle whose radius is ', . Show also that if two tangents to the circle be drawn from A, their chord of contact passes through B. Ex. 364. Four points A, B, A', B' are given in a plane; prove that there are always two positions of a point C in the plane such that the triangles CAB, CA'B' are similar, the equal angles being denoted by corresponding letters. Ex. 365. Three chords AA', BB', CC of a circle are concurrent. Show that the product of the lengths of the chords AB', BC, CA' is equal to that of the chords BA', CB', AC Ex. 366. Show that a line cannot be divided harmonically by two circles which cut orthogonally, unless it passes through one or other of the centres. Ex. 367. The bisectors of the angles A, B, C of a triangle cut the opposite sides in X1, X2; Yi, Y2; Zi, Z2 respectively. Show that the circles on the lines XiX2, Y2, Z1Z.i as diameters have a common chord. Ex. 3...
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Add this copy of Modern Geometry to cart. $16.27, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
Add this copy of Modern Geometry to cart. $27.44, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
Add this copy of Modern Geometry to cart. $44.02, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2010 by Nabu Press.
