1. consider a right triangle drawn on a page with sides of lengths 3 cm, 4 cm, and 5 cm.
a. describe a sequence of straightedge and compass constructions that allow you to draw the circle that circumscribes the triangle. explain why your construction steps successfully
accomplish this task.
b. what is the distance of the side of the right triangle of length 3 cm from the center of the circle that
circumscribes the triangle?
c. what is the area of the inscribed circle for the triangle?

a)

First we need to draw a perpendicular bisector of the side AB. Next, draw a perpendicular bisector of the side BC. We use the same method above.Now, put 0 where the bisectors intersect.Finally, put one part of the compass on 0 an the other part on C and draw the circle.

b)

c) R = 1 cm.

Step-by-step explanation:

Let's define:

AB: distance of the side with length 3 cm

AC: distance of the side with length 4 cm

BC: distance of the side with length 5 cm

a)

First we need to draw a perpendicular bisector of the side AB. We just put he compass in A, with any distance and trace two semicircle between AB.Next, draw a perpendicular bisector of the side BC. We use the same method above.Now, put 0 where the bisectors intersect.Finally, put one part of the compass on 0 an the other part on C and draw the circle.    

b)

In a right triangle the hypotenuse of the triangle is the diameter of its circumscribe circle, so the radius of the circle is equal to half of the hypotenuse of the right triangle.

So if we draw a line from the center to the middle of the AB we will have new triangle, with sides BC/2, AB/2 and x, when x is the distance from the center to the length 3 cm. Therefore x will be:

c)      

We need to find the radius of the circle to find the area.

So we can use this formula.

A is the triangle area, it is AC*AB/2 =  6 cm²

P is the triangle perimeter, it is AC+AB+BC = 12 cm

R is the radius of the inner circle.

Then, R = 2*6/12 = 1 cm.

Have a nice day!

A. p = 2(l + w)p/2 - l = ww = p/2 - l b. while isolating the variable w in the equation, i first divided both sides by 2 and then i subtracted l from both sides. i hope this .

Answer: d. 39 cmin the diagram, the approximate length of the minor arc de is 39 centimetres.step-by-step explanation: the formula for the length of an arc in a circle is as displayed below.let the length of the minor arc de = xx = 2( pi )r × angle of sector / 360°from this, we will substitute the values given from the problem into the formula to obtain the length of the minor arc de.x = 2( pi )r × angle of sector / 360°r = radius = 25cmpi as an approximate value = 3.14angle of sector = 120°x = 2( 3.14 )( 25 ) × 120° / 360°x = 157 × 1 / 4x = 39.25x = 39 ( rounded to the nearest whole number as an approximate value )