Secant and Secant Segments
1.
In geometry, segments such as XY and XZ are called ___________________.
2.
Do you see a relationship among the segment measures?
3.
[b]Do the following calculations:[/b]
4.
XY + AX = ___________[br][br]XZ + BX = ____________
5.
Are the sums equal?
6.
XY - AX = ___________[br][br]XZ - BX = ___________
7.
Are the differences equal?
8.
XY * AX = __________[br][br]XZ * BX = __________
9.
Are the products equal?
10.
Grab point X and move it around circle O. What do you notice about the products of XY * AX and XZ * BX?
11.
Make a conjecture (statement) about the products of secant segments using the names of the segments in the above circle.
Inscribed Right Triangles
Inscribed Right Triangles
1.
Are A-C-D collinear?
2.
What is the relationship of AD to the [b]circle[/b]? Explain.
3.
What is the relationship of AD to [math]\bigtriangleup[/math]ABD? Explain.
4.
What is the relationship between the hypotenuse and the diameter of the circle?
7.
Grab and move point B around the circle.
6.
Does the measure of [math][/math]<ABD change?
7.
Does the position of AD change?
8.
What can you conclude about any right triangle inscribed in a circle?
9.
[b]Fill in the blank. [/b]If a triangle has one leg as the diameter, then it is a ___________ triangle.
10.
[b]Extension Question: [/b]Given a right, triangle, what is the easiest way to find the center of a circumscribed circle?