Given:
oh
⊥
bc
, ob=10,
oh=6, ef=9, ab=2
find: ae.

AE=3

Step-by-step explanation:

1. Consider right triangle BOh. In this triangle, OB=10 (hypotenuse), OH=6 (leg), then by the Pythagorean theorem,

2. Since OH⊥BC, then BC=2BH=16.

3. Use the secants property: If two secant segments are drawn to a circle from the same external point, the product of the length of one secant segment and its external part is equal to the product of the length of the other secant segment and its external part.

Thus,

So,

The segment cannot be of negative length, therefore, AE=3.

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