Line segment on is perpendicular to line segment ml, and pn = 10. what is the area of triangle mol?

Given a circle with radius = 25 and the distance of the chord ML from the circumference = 10.
i.e. ON = 25 and PN = 10

But ON = OP + PN
25 = OP + 10

Thus OP = 25 - 10 = 15

Now to find the length of line segment MP, we note that triangle MOP is a right triangle with MO as the hypothenus.

MO is a radius to the circle, hence MO = 25 and OP = 15

Recall that the pythagoras rule for finding the length of the hypothenus says that the square of the length of the hypothenus is equal to the sum of the square of the lengths of the other two legs of a right triangle.

Thus,

Recall that the area of a triangle is given by half of the base times the height.

Therefore, the area of triangle MOL is given by half ML times OP = MP times OP = 20 x 15 = 300 square units.

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.