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

Solution:

From the question,

it is given that line segment ON is perpendicular to line segment ML, and PN = 10.

From the given figure,

the triangle MOL is an isosceles triangle.

Then,

MO = OL = 25 units… [because radius of circle]

ON = 25 units

ON = OP + PN

25 = OP + 10

By transforming we get,

OP = 25 - 10

OP = 15 units

Now we have to find base MP

Triangle MPO is a right-angle triangle.

By applying Pythagoras theorem,

MO² = MP² + PO²

25² = MP² + 15²

By transforming we get,

MP² = 25² - 15²

MP² = 400

MP = √400

MP = 20

So, ML = 2MP

ML = 2 × 20

ML = 40 units

Finally,

we have to find the area of triangle MOL

A = 1/2 ML × PO

A = 1/2 × 40 × 15

A = 300 unit²

Therefore, the area of the triangle MOL is 300 square units.

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Line segment ON is perpendicular to line segment ML, and PN = 10. What is the area of triangle MOL?

Summary:

The line segment ON is perpendicular to line segment ML, and PN = 10. The area of the triangle MOL is 300 square units.