Triangle inscribed on circle proof I am missing something

In summary, the problem is to prove that AE is an altitude in a triangle inscribed in a circle. The approach involves drawing lines OB and OC to create similar triangles and using the congruence of radii and angles to prove that AE is perpendicular to BC. Additional information is needed to show that E is the midpoint of BC. This can be done by proving that any perpendicular bisector of a secant to a circle goes through the center of the circle.
  • #1
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Triangle inscribed on circle proof...I am missing something :(

Homework Statement


I have provided a link to the problem below
http://imageshack.us/a/img854/4143/photo1lsd.jpg

I need to prove AE is an altitude on this proof

Homework Equations


all radii are congruent, cpctc, ASA, congruent supplementary angles are right angles


The Attempt at a Solution



I know that I need to draw in lines OB and OC for use in similar triangles and that once congruence is proven I can quickly show the supplementary angles are congruent and thus AE is an altitude.. I feel like this needs additional information saying E is the midpoint of BC...hence me being stuck. Any help would be appreciated.
 
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  • #2


Do you know, or can you prove, that any perpendicular bisector of a secant to a circle goes through the center of the circle?
 

1. What is a triangle inscribed on a circle?

A triangle inscribed on a circle is a triangle whose three vertices are located on the circumference of a given circle.

2. How do you prove that a triangle is inscribed on a circle?

To prove that a triangle is inscribed on a circle, you can use the theorem which states that an angle inscribed in a semicircle is always a right angle. If all three angles of a triangle are inscribed in a semicircle, then the triangle must be inscribed on the circle.

3. What is the significance of a triangle inscribed on a circle?

A triangle inscribed on a circle has several properties that make it useful in various mathematical and geometric applications. For example, the lengths of the sides of the triangle and the angles formed can be used to calculate other properties such as the area and perimeter of the triangle.

4. Can a triangle be inscribed on any circle?

Yes, any circle can have a triangle inscribed on it. The only requirement is that the three vertices of the triangle must lie on the circumference of the circle.

5. How can the proof of a triangle inscribed on a circle be applied in real life?

The proof of a triangle inscribed on a circle has practical applications in fields such as architecture, engineering, and surveying. It can also be used in solving geometry problems and in developing new theorems and proofs.

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