<prompt> Acha overlineCH iwe mwinuko wa pembetatu ABC. Acha R, na S, ziwe pointi ambapo miduara iliyoandikwa katika pembetatu ACH, na BCH ni tanjiti hadi overlineCH. Ikiwa AB 1995,, AC 1994,, na BC 1993,, basi RS, inaweza kuonyeshwa kama mn,, ambapo m, na n, ni nambari kamili kuu kiasi. Tafuta m n,.  <response>: asy unitsize48; jozi A,B,C,H; A8,0; Basili; C3,4; H3,0; kuchoraA--B--C--mzunguko; kuchoraC--H; leboA,A,SE; leboB,B,SW; leboC,C,N; leboH,H,NE; choramduara2,1,1; jozi xintersectionpointsC--H,mduara2,1,1; nukta x0; leboS,x0,SW; kuchoramduara4.29843788128,1.29843788128,1.29843788128; jozi yintersectionpointsC--H,mduara4.29843788128,1.29843788128,1.29843788128; nukta y0; leboR,y0,NE; lebo1993,1.5,2,NW; lebo1994,5.5,2,NE; lebo1995,4,0,S; asyKutoka kwa Nadharia ya Pythagorean, AH2CH219942, na 1995-AH2CH219932.Kuondoa milinganyo hiyo miwili inatoa AH2-1995-AH23987.Baada ya kurahisisha, tunaona kwamba 21995AH-199523987, au AHfrac19952frac398721995.Kumbuka kuwa AHBH1995.Kwa hivyo tuna hiyo BHfrac19952-frac398721995.Kwa hivyo AH-BHfrac39871995.Sasa kumbuka kuwa RSHR-HS, RHfracAHCH-AC2, na HSfracCHBH-BC2.Kwa hivyo tuna RSleft fracAHCH-AC-CH-BHBC2 rightfracAH-BH-199419932.Tunachomeka AH-BH na kurahisisha, tuna RSfrac199219952frac332665 rightarrow 332665997. 