Question

Line segments MP and ML are perpendicular chords in circle O. MP = 10 and ML = 24.

Answer 1

The diameter of this circle at the same time hypotenuse of triangle LMP
|LM|²=24²+10²
|LM|=√(676)=26 - diameter
so radius =26/3=13
-The radius of circle O is 13.
-LP is a diameter of circle O.
-∠LMP intercepts a semicircle.

Answer 2

Answer:

Option A, C and D are correct choices.

Step-by-step explanation:

We have been given that line segments MP and ML are perpendicular chords in circle O. MP = 10 and ML = 24.                      

Let us see our given choices one by one.

A. The radius of circle O is 13.

We can see from our given circle that line LP passes through the center of circle, therefore, LP is diameter of our circle.

Let us find the length of diameter of circle, then divide by 2 get the radius of our circle.

We will use Pythagoras theorem to find the length of diameter as:

$PL^2=ML^2+MP^2$

$PL^2=24^2+10^2$

$PL^2=576+100$

$PL^2=676$

Let us take square root of both sides of our equation.

$PL=\sqrt{676}$

$PL=26$

Therefore, the diameter of our given circle is 26 units.

$\text{Radius of the circle}=\frac{26}{2}$

$\text{Radius of the circle}=13$

Therefore, option A is the correct choice.

B. The diameter of circle O is 34.

Since the diameter of our circle is 26 units, therefore, option B is not correct.

C. LP is a diameter of circle O.

Since line LP passes through the center of circle O, therefore, LP is diameter of our circle and option C is correct as well.

D. ∠LMP intercepts a semicircle.

Since an inscribed angle is half the measure of central angle, therefore, measure of central angle corresponding to arc LMP will be 2*80=180 degrees.

Since Arc LMP is 180 degrees and measure of semicircle is always 180 degrees, therefore, angle LMP intercepts a semicircle and option D is correct choice.

E. The measure of arc LP is 90°.

Since the measure of arc LMP is 180 degrees, therefore, measure of arc LP will be also 180 degrees, therefore, option E is not correct.