The vertices of a triangle lie on the circumference of a circle. If its sides are 2.5 cm, 6 cm, and 6.5 cm, what is the area of the circle (in c
m
2
)?

The area of the circle is approximately 33.183 cm²

Step-by-step explanation:

The sides of the inscribed triangle are 2.5 cm, 6 cm, and 6.5 cm

By cosine rule, we have;

6.5² = 6² + 2.5² - 2 × 6 × 2.5 × cos A

2 × 6 × 2.5 × cos A = 6² + 2.5² - 6.5² = 0

∴ cos(A) = 0

A = cos⁻¹(0) = 90°

The angle subtended at the center = 2 × Angle subtended at the circumference

Therefore, angle at the center = 2 × 90° = 180°

The 6.5 cm side forms an angle of 180° (a straight line) at the center of the circle and therefore, the 6.5 cm side = The diameter of the circle

The radius of the circle = 1/2 × The diameter of the circle = 1/2 × 6.5 cm = 3.25 cm

The area of the circle = π × r² = π × 3.25² ≈ 33.183 cm².

okay wait before i answer, is this for your points on a graph?

the most boring ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.