Triangle inscribed on circle proof I am missing something

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SUMMARY

The discussion focuses on proving that line segment AE is an altitude in a triangle inscribed in a circle. The user references the need to draw lines OB and OC to establish similar triangles and uses concepts such as congruent supplementary angles and the ASA (Angle-Side-Angle) theorem. The user expresses uncertainty about the necessity of stating that point E is the midpoint of segment BC to complete the proof. Additionally, the user seeks clarification on whether the perpendicular bisector of a secant to a circle always passes through the circle's center.

PREREQUISITES
  • Understanding of triangle congruence theorems, specifically ASA (Angle-Side-Angle).
  • Knowledge of properties of circles, including congruent radii and perpendicular bisectors.
  • Familiarity with the concept of supplementary angles and their properties.
  • Ability to analyze geometric proofs involving inscribed angles and altitudes.
NEXT STEPS
  • Research the properties of perpendicular bisectors in relation to circles.
  • Study the ASA theorem and its applications in geometric proofs.
  • Explore the concept of similar triangles and their relevance in proving congruence.
  • Investigate the relationship between midpoints and altitudes in triangle geometry.
USEFUL FOR

Students studying geometry, particularly those working on proofs involving triangles inscribed in circles, as well as educators seeking to clarify geometric concepts related to altitudes and bisectors.

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

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