SOLUTION: please help me whith geometric problem thanks in the below point A is 8ft away from a circle of Radius =5ft line AB is tangential to the circle what is the distrance AB?

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Question 595931: please help me whith geometric problem thanks in the below point A is 8ft away from a circle of Radius =5ft line AB is tangential to the circle what is the distrance AB?
Answer by solver91311(24713) (Show Source):
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Solution depends upon the assumption that B is the point of tangency of the line containing the segement AB.

Label the center of the circle as point O. Construct the radius OB and the segment OA. A radius to a point of tangency is perpendicular to the tangent line, hence triangle AOB is a right triangle.

Label the point of intersection of the circle and the line segment OA as point D. Note that OD is a radius so OD measures 5 ft. Note that DA is given as 8 ft. Finally, the measure of OA is the sum of the measures of OD and DA, which is to say 13 feet.

Note that OB is a radius and therefore measures 5 ft.

Note that you have a right triangle where the short leg measures 5 ft and the hypotenuse measures 13 ft.

Use the Pythagorean Theorem to calculate the measure of the other leg of the triangle, namely the segment AB.

Quick method: Recall the Pythagorean triple where 5 is the smallest value and 13 is the largest value. Use the third value as the measure of AB.

John

My calculator said it, I believe it, that settles it