1. ## Fill in the Blank(about triangles)

1. In a right triangle the (a)________of the triangle intersect at a point on the hypotenuse, the (b)________intersect at a point inside the triangle, and the altitudes of the triangle intersect at a (c)______of the triangle.

2. An isosceles triangle has sides of length 5, 5, and 8.
(a) What is the length of the median to the base?

(b) When the three medians were drawn, the median to the base is
divided into segments with lengths ______ and ______.
Then solve this problems if you can...Thanks again...^^;;

1. Find the area of a rectangle with length 12 inscribed in a circle with

2. Find the area of a square with radius 9. (By the way, what is the radius
in the regular polygon?)

3. The areas of two circles are 100 pie and 36 pie. Find the ratio of their
radii and the ratio of their circumference.

(Have a nice day....~!!!!^0^*)

2. Originally Posted by sarayork

1. In a right triangle the (a) perpendicular bisectors of the sides of the triangle intersect at a point on the hypotenuse, the (b) angle bisectors and the medians intersect at a point inside the triangle, and the altitudes of the triangle intersect at a (c) vertex of the triangle.

2. An isosceles triangle has sides of length 5, 5, and 8.
(a) What is the length of the median to the base?

(b) When the three medians were drawn, the median to the base is
divided into segments with lengths 2 and 1.
Then solve this problems if you can...Thanks again...^^;;

1. Find the area of a rectangle with length 12 inscribed in a circle with

2. Find the area of a square with radius 9. (By the way, what is the radius
in the regular polygon?)

3. The areas of two circles are 100 pie and 36 pie. Find the ratio of their
radii and the ratio of their circumference.
to #2
a) Use Pythagorean theorem: One leg of the isosceles triangle is the hypotenuse, the median and the half base are the legs in a right triangle:

$m = \sqrt{25-16}=3$

b) A median in a triangle is divided by the remaining medians into 2 parts with the ratio 2:1 from the vertex.

#1: If the rectangle is inscribed into a circle the diameter of the circle is a diagonal of the rectangle. Use Pythagorean theorem to calculate the length of the other side of the rectangle:

$s = \sqrt{(2 \cdot 7.5)^2 - 12^2} = 9$ . Now calculate the area of the rectangle.

#3: The area of a circle is calculated by:

$a = \pi \cdot r^2$ . You have:

$a_1 = \pi \cdot 100 = \pi \cdot 10^2~\implies~ r = 10$

$a_2 = \pi \cdot 36 = \pi \cdot 6^2~\implies~ r = 6$ . and therefore

$\frac{r_1}{r_2}=\frac{10}{6} = \frac53$

The perimeter is calculated by: $p = 2\pi \cdot r$

Calculate the perimeter $p_1$ and $p_2$ and build the ratio:

$\frac{p_1}{p_2}=\frac{2\pi \cdot 10}{2\pi \cdot 6} = \frac53$ or more generally:

$\frac{p_1}{p_2}=\frac{r_1}{r_2}$