Which statement is valid when a circumscribed circle of an acute triangle is
constructed?
A. The longest side of the triangle lies on the diameter of the circle.
B. The circle is drawn inside of the triangle and touches all three sides.
C. The center of the circle is in the interior of the triangle.
D. The vertices of the triangle lie on the circle.

Explanation:

For any acute triangle, the center of the circle is always inside the triangle.

For any right triangle, the center of the circle is the midpoint of the hypotenuse. The hypotenuse is the diameter of the circle.

For any obtuse triangle, the center of the circle is outside the triangle.

Let's look at the answer choices more closely

A. False. This is only true if we have a right triangle as mentioned earlier.

B. False. This describes an inscribed circle.

C. True. As stated earlier.

D. True. This is based on how the circumscribed triangle is defined. It is set up to be the circle that goes through all three vertex points of a triangle. In other words, it is the smallest circle to completely enclose the given triangle.

solution:

as, mean is defined as sum of all the observations divided by total number of observations.

and , median is mid value of the data whether arranged in ascending order or descending order.

consider, roadsters:

2,3,4,5,6,7,8,9

mean =

also, median= , because number of observations is even, so median is mean of two mid values.

now, coming to bandits

2,3,4,5,6

mean =  

median = 4, as number of observations is odd.

so, roadsters has greater median as well mean than bandits.

→option a is true about the repairs performed on 2 types of cars:

bandits have lower median and mean than roadsters.