Question

1. Prove the general formula for inversion in a circle C centered at zo with radius r. In particular, show in this case that p2 ic(z) + 20 (z – zo)

theres no other information needed? im not sure what youre wanting

Answer 1

ANSWER! n. Claim: 0. Op. op.ge 2. ICCP); goed 아동 (2-20) zo pi Since In version formula o o.p. op':02 proof Suppose point perpendicular to op intersect circle at A then, LOPA LQAP) - 90% on other, Op = (POA is common The triangles AOPA and DOAP' are similar OL: OA DA DP' → Op. op's (OA) - 92 ->01) Circle C is centered at Zo. and has madiu9 8 Let z (P,9) be any point to undestand better from giver data, say, Z=P: (Diz) then, op: Izp-p] = 160,6)-(P,9)) (P-a)2+(96)2 op. VCP-)2+(9-572 Allies as op! .pl. (0, b) + op (P-0,9-b) OP 22 Zo + (P-2,9-6) (p-1)319-612

+ (2-20) (2-2)(2-2) (2-2) Hence proved. 4. Given, let Ti is inversion in Circle 1Z) = my Let Ta is inversion in Circle 121=10 NOW, Tic2): į and Tec2): TI (79 CZ)) = TI(Y2) - Z TACTI(z)) - T2(1): Z } both are diabetion with all because, TZ): Az is dilation the converse part. is not true any dilation can't show as composition of too inverse. Actually if a is not equal to 1 n dilation then write it composit on of LOO inverse. Take dilation T(z): 21 then it can be written as composition of inverse TILZ)- and Tące): Ž tudo Thanung you please give like it helps to motivate me to do moro Work friend