posted by .

Let AB be the diameter of a circle, and let point P be a point on AB. Let CD be a chord parallel to AB. Prove that PA^2 + PB^2 = PC^2 + PD^2

It can be solved using geometry methods (no trig). Anyway, I figured out that PA^2 +PB^2 = 2OP^2 + 2OB^2. However, I cannot find right triangles to help to find PC^2+PD^2. Oh, and I got a hint: "The problem involves sums of squares of lengths. What should you be looking for (or building) in the problem?"

## Similar Questions

1. ### Geometry

Prove that the tangents to a circle at the endpoints of a diameter are parallel. State what is given, what is to be proved, and your plan of proof. Then write a two-column proof. Hint draw a DIAGRAM with the points labeled. Can some …
2. ### math

The equation of a circle with centre O(0,0) is x^2+y^2=40. The points A(-2,6) and B(-6,-2) are endpoints of chord AB. DE right bisects chord AB at F. a)Verify that the centre of the circle lies on the right bisector of chord AB. b)Find …

6. ### Circle geometry

Please help Explain how I figure this out. A circle has diameter 70cm. A chord in the circle is 50cm long. How far is the chord from the center of the circle?
7. ### math

1. A(-3;4) is a point on a circle with centre at the origin. a.determine the coordinates of B, if AB is a diameter. b. Show that point C(0;5) lies on this circle. c.show that ACB has a magnitude of 90degrees. 2.a.ddetermine the equation …
8. ### math

Is the following statement true or false?
9. ### MATH HELP MS SUE OR SOMEONE

Is the following statement true or false?
10. ### math

AB is a chord of a circle with center O, C is the midpoint of the chord AB, extend OC to the point D on the circle. If OC=CD, what is the measure of angle AOB?

More Similar Questions