Key words: Geometry, Unusual geometry, Math, Physics, Chemistry, High school, Geometry Olympiads, Free Geometry, Euclidean Geometry, Calculus, Geometric Construction. Oh yes, going-nowhere discussions, haikus, and poems too.
Also this shows that BP=PC
Let x=BPRPQ=180-(90-B)-(90-C)=B+C=180-APR=x.sin(B); PQ=(BC-x).sin(C)ThenA(PQR)=PQ*PR*sin(RPQ)/2= x*(BC-x)*sin(A)*sin(B)*sin(C)/2Maximum occurs when x=BC/2 andmaxium(A(PQR))=BC^2*sin(A)*sin(B)*sin(C)/8César LozadaVenezuela
Also this shows that BP=PC
ReplyDeleteLet x=BP
ReplyDeleteRPQ=180-(90-B)-(90-C)=B+C=180-A
PR=x.sin(B); PQ=(BC-x).sin(C)
Then
A(PQR)=PQ*PR*sin(RPQ)/2=
x*(BC-x)*sin(A)*sin(B)*sin(C)/2
Maximum occurs when x=BC/2 and
maxium(A(PQR))=BC^2*sin(A)*sin(B)*sin(C)/8
César Lozada
Venezuela