<prompt> Acha H iwe kitovu cha pembetatu ABC. Kwa pointi zote P kwenye mduara wa pembetatu ABC,PA2 PB2 PC2 - PH2ni thabiti. Onyesha hili lisilobadilika kulingana na urefu wa upande a, b, c na mduara wa R wa pembetatu ABC.  <response>: Acha kipenyo cha O cha pembetatu ABC kiwe asili, kwa hivyo overrightarrowP R. Pia, overrightarrowH overrightarrowA overrightarrowB overrightarrowC. KishaanzaalignPA2 mshale wa kulia zaidiP - ushale uliopitilizaA2 mshale uliopitilizaP - ushale uliopitilizaA cdoti mshale uliopitilizaP - ushale uliopitilizaA mshale wa kulia zaidiP cdot mshale wa kulia zaidiP - 2 ushale uliopitilizaA cdot ushale uliopitilizaP ushale uliopitilizaA cdot ushale uliopitilizaA R2 - 2 mshale wa kulia zaidiA cdot mshale wa kuliaP R2 2R2 - 2 mshale wa kulia juuA cdot mshale wa kuliaP.mwishoalignVile vile,anzaalignPB2 2R2 - 2 mshale ulio kulia juuB cdoti mshale wa kuliaP, PC2 2R2 - 2 mshale wa kulia juuC cdot mshale wa kuliaP,mwishoalignnaanzaalignPH2 arrow kuliaP - overrightarrowH2 mshale ulio juu zaidiP - ushale unaozidi kuliaA - ushale uliopitilizaB - ushale uliopitilizaC2 overrightarrowA cdot overrightarrowA overrightarrowB cdot overrightarrowB overrightarrowC cdot overrightarrowC overrightarrowP cdot overrightarrow P quad 2 overrightarrowA cdot overrightarrowB 2 overrightarrowA cdot overrightarrowC 2 overrightarrowB cdot overrightarrowC - 2 overrightarrow A cdoti mshale ulio kulia zaidiP - 2 mshale ulio kulia zaidiB cdot ushale uliopitilizaP - 2 ushale uliopitilizaC cdot ushale uliopitilizaP R2 R2 R2 R2 quad 2 kushoto R2 - fraca22 kulia 2 kushoto R2 - fracb22 kulia 2 kushoto R2 - fracc22 kulia - 2 arrowoverrightarrowA cdot overrightarrowP - 2 overrightarrowB cdot overrightarrowP - 2 kishale zaidiC cdot mshale wa kuliaP 10R2 - a2 - b2 - c2 - 2 arrowoverrightarrowA cdot overrightarrowP - 2 overrightarrowB cdot overrightarrowP - 2 overrightarrow C cdot mshale wa kuliaP.mwishoalignHivyo,PA2 PB2 PC2 - PH2 a2 b2 c2 - 4R2. 