we know that
Triangle MOL is an isosceles triangle
because
[tex] MO=OL=radius\ of\ circle=25\ units [/tex]
[tex] ON=25\ units [/tex]
[tex] ON=OP+PN\\ 25=OP+10\\ OP=25-10\\ OP=15\ units [/tex]
Find the base MP
Applying the Pythagorean Theorem in the right triangle MPO
[tex] MO^{2} =MP^{2}+PO^{2}\\ MP^{2}=MO^{2}-PO^{2}\\ MP^{2}=25^{2}-15^{2}\\ MP^{2}=400\\ MP=20\ units [/tex]
[tex] ML=2*MP\\ ML=2*20\\ ML=40\ units [/tex]
Find the area of triangle MOL
[tex] A=\frac{1}{2}ML*PO\\ \\ A=\frac{1}{2}*40*15\\ \\ A=300\ unit^{2} [/tex]
therefore
the answer is
the area of triangle MOL is
[tex] 300 [/tex] square units
