The image below is a triangle drawn inside a circle with center o: a triangle is shown inscribed inside a circle. the leg of the triangle labeled 8 inches passes through the center of the circle, o. the other two legs are labeled as 4 inches and 5 inches. which of the following expressions shows the area, in square inches, of the circle? (π = 3.14) 3.14 ⋅ 42 3.14 ⋅ 52 3.14 ⋅ 5 3.14 ⋅ 22

A.

Step-by-step explanation:

We have been given that a triangle is inscribed inside a circle. The leg of the triangle labeled 8 inches passes through the center of the circle, O. The other two legs are labeled as 4 inches and 5 inches.

The leg with 8 inches length passes through the center, so it will be the diameter of the circle.

To find the area of the circle, we will divide diameter by 2 to find radius of circle.

Upon looking at our given choices, we can see that option A is the correct choice.

d

step-by-step explanation:

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.