Given: BAL is a right triangle at A. O is the midpoint of [BL]. The circle of diameter [BO] cuts [BA] at I. Show that I is the midpoint of [AB].
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Originally Posted by Pythagorean Theorem Given: BAL is a right triangle at A. O is the midpoint of [BL]. The circle of diameter [BO] cuts [BA] at I. Show that I is the midpoint of [AB]. 1. Triangle BIO is a right triangle with because I is placed on the Thales circle over BO. 2. You have 2 similar triangles: 3. Use proportions.
Here is a second way. The being inscribed in a semi-circle is a right angle. Therefore, so by the midpoint theorem is the midpoint of .
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