<prompt> Katika pembetatu ABC, BC 4, AC 3 sqrt2, na angle C 45circ. Miinuko AD, BE, na CF inakatiza katikati mwa orthocenter H. Pata AH:HD.  <response>: Kwa kuwa angle C 45circ, pembetatu ACD ni 45circ-45circ-90circ pembetatu, ambayo ina maana AD CD ACsqrt2 3. Kisha BD BC - CD 4 - 3 1.asyukubwa wa kitengo 1 cm;jozi A, B, C, D, E, F, H;A 1,3;B 0,0;C 4,0;D A tafakariB,CA2;E B tafakariC,AB2;F C tafakariA,BC2;H kiendeleziB,E,C,F;kuchoraA--B--C--mzunguko;kuchoraA--D;kuchoraB--E;kuchoraC--F;leboA, A, N;leboB, B, SW;leboC, C, SE;leboD, D, S;leboE, E, NE;leboF, F, NW;leboH, H, SE;asyPia, angle EBC 90circ - angle BCE 45circ, hivyo pembetatu BHD ni 45circ-45circ-90circ pembetatu. Kwa hivyo, HD BD 1. Kisha AH AD - HD 3 - 1 2, hivyo AH:HD 2 . 