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Math·Geometry and Trigonometry·Circles

hard

A circle has its center at $(3,7)$. Line $t$ is tangent to the circle at the point $(a,-4)$. The slope of line $t$ is $\frac{5}{4}$.

What is the value of $a$?

A

$-\frac{43}{4}$

B

$-\frac{29}{5}$

C

$\frac{67}{4}$

D

$\frac{43}{4}$