Question

Line segment ON is perpendicular to line segment ML, and PN = 10.

What is the area of triangle MOL?

200 square units
250 square units
300 square units
500 square units

Answer 1

300 sq units. hope it will help you!

Answer 2

we know that

Triangle MOL is an isosceles triangle

because

`MO=OL=radius\ of\ circle=25\ units`

`ON=25\ units`

`ON=OP+PN\\ 25=OP+10\\ OP=25-10\\ OP=15\ units`

Find the base MP

Applying the Pythagorean Theorem in the right triangle MPO

`MO^(2) =MP^(2)+PO^(2)\\ MP^(2)=MO^(2)-PO^(2)\\ MP^(2)=25^(2)-15^(2)\\ MP^(2)=400\\ MP=20\ units`

`ML=2*MP\\ ML=2*20\\ ML=40\ units`

Find the area of triangle MOL

`A=(1)/(2)ML*PO\\ \\ A=(1)/(2)*40*15\\ \\ A=300\ unit^(2)`

therefore

the answer is

the area of triangle MOL is

`300` square units