Math / Geometry

Question16. $\overline{W Q}$ and $\overline{T Q}$ are tangent to circle $R$ . WQ $=3 x-4$ and $T Q=5 x-18$ . Find the value of $x$ .

Studdy Solution

STEP 1

1. $\overline{WQ}$ and $\overline{TQ}$ are tangent to circle $R$ from the same external point $Q$ .
2. Tangents drawn from an external point to a circle are equal in length.

STEP 2

1. Set the lengths of the tangents equal.
2. Solve the equation for $x$ .

STEP 3

Since $\overline{WQ}$ and $\overline{TQ}$ are tangents from the same external point $Q$ , they are equal in length. Set the expressions for the lengths equal:
$3x - 4 = 5x - 18$

STEP 4

Solve the equation for $x$ :
$3x - 4 = 5x - 18$
Subtract $3x$ from both sides:
$-4 = 2x - 18$
Add 18 to both sides:
$14 = 2x$
Divide both sides by 2:
$x = 7$
The value of $x$ is:
$\boxed{7}$

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