A Key to the Exercises And Examples Contained in a Text book of Euclids Element

H S Henry Sinclair Hall

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Now AP is perp. To OP. . . AP touches the fixed whose centre is O and radius OR.
13. Let A be the centre of the outer, and B of the inner fixed . Let P be the centre of any third touching the first at D and the second at E. Then shall AP + BP be constant. Let r u T r s denote the radii of the three s . Then the points A, P, D and B, E, P are collinear [in. 11 and 12].
And AP + BP = r-j r 3 + r 2 + r 3 = r x + r 2 .
NOTE. This problem is a special case of the following: If any two circles are to...uched one internally and one externally by a third circle, the sum or difference of the distances of this third circle from the centres of the given circles is constant.
14. Let PA, PB be any pair of tangents containing the given angle. Take C the centre of the 0, and join CA, CP. Now CP bisects the L. APB [m. 17, Cor. ]. Hence in the A CAP, the _ S CAP, CPA, and the side CA are constant; /. CP is constant [i. 26]. . . The locus of P is a concentric 0.
15. Let A and B be the centres of the two given s, X and Y the given st.

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