What is the area (in cm²) of the circumcircle of a triangle whose sides are 6 cm, 8 cm and 10 cm respectively?

In a trapezium, one diagonal divides the other in the ratio 2 :9. If the length of the larger of the two parallel sides is 45 cm, then what is the length (in cm) of the other parallel side?

In the given figure, ABCD is a square inscribed in a circle of radius 4 cm. CD is produced till point E. From E a tangent is drawn to the circle at point B.  What is the length (in cm) of AE?

In triangle ABC, F is the centroid. If AB=11 cm, BC=14 cm and AC=7 cm, then what is the value (in cm) of EF?

If $$ {x+3y-{2z\over 4}}=6$$ , $$ {x+{2\over 3}}(2y+3z)=33$$ and $$ {1\over 7}{(x+y+z)+2z=9}$$, then what is the value of $$ {46x+131y}$$?

$${3x+4y-2z+9=17},{7x+2y+11z+8=23}$$ and $$ {5x+9y+6z-4=18}$$ then what is  the value of $$ {x+y+z-34}$$?

If $${a+b=10}$$ and $$ \sqrt{a\over b}-13=-\sqrt{b\over a}-11$$, then what is the value of $${3ab+4a^2+5b^2}$$?

If $$ {3\sqrt{{1-a}\over{a}}}+9={19-3\sqrt{{a}\over{1-a}}}$$, then what is the value of a?