• If asece + btane + c = D 0 and psece + qtan e + r = 0 then prove that - (br-qc) - (pc-ar) = (aq-bp)

If a sec theta+b tan theta+c=0 and p sec theta+q tan theta+r=0 prove that (br-qc)^(2)-(pc-ar)^(2)=(aq-bp)^(2)

If a sec theta+b tan theta+c=0 and p sec theta+q tan theta+r=0, prove that (br-qc)^(2)-(pc-ar)^(2)=(aq-bp)^(2)

If asectheta+btantheta+c=0andpsectheta+qtantheta+r=0 , then (br-qc)^(2)-(pc-ar)^(2)=?

In Figure, /_\ A B C and /_\ D B C are on the same base B C . If A D and B C intersect at O , prove that (A r e a\ ( A B C))/(A r e a\ ( D B C))=(A O)/(D O) .

If the points (a, 0), (b,0), (0, c) , and (0, d) are concyclic (a, b, c, d > 0) , then prove that ab = cd .

If the points (a, 0), (b,0), (0, c) , and (0, d) are concyclic (a, b, c, d > 0) , then prove that ab = cd .

If the points (a, 0), (b,0), (0, c) , and (0, d) are concyclic (a, b, c, d > 0) , then prove that ab = cd .

In A B C , A D and B E are altitudes. Prove that (a r( D E C))/(a r( A B C))=(D C^2)/(A C^2)

If p + q + r = a + b + c = 0, then the determinant |{:(pa,qb,rc),(qc,ra,pb),(rb,pc,qa):}| equals