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# geometry

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Let XY be a tangent to a circle, and let XBA be a secant of the circle, as shown below. If AX = 16 and XY = 9, then what is AB?

Apr 4, 2022

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If AX = 16 and XY = 9, then what is AB?

Hello Guest!

secant-tangent theorem

For every point X outside a circle: The square of the length of the tangent from point X to the point of tangency is equal to the product of the segments of a straight line through the circle from point X to the points of intersection with the circle.

$$9=\sqrt{(16-AB)\cdot 16}\\ 81=16^2-16\cdot AB\\ AB=\dfrac{16^2-81}{16}\\ \color{blue}AB=10.9375$$

!

Apr 4, 2022
edited by asinus  Apr 4, 2022