Question

a is equidistant to b and c. find bd. a b 2x + 6 d x + 8 c bd = ?

Explanation:

Step1: Recall the Perpendicular Bisector Theorem

Since \( A \) is equidistant to \( B \) and \( C \), and \( AD \perp BC \) (right angle at \( D \)), \( AD \) is the perpendicular bisector of \( BC \). Thus, \( BD = DC \).

Step2: Set Up the Equation

Set \( 2x + 6 = x + 8 \).

Step3: Solve for \( x \)

Subtract \( x \) from both sides: \( 2x - x + 6 = 8 \), so \( x + 6 = 8 \). Then subtract 6 from both sides: \( x = 8 - 6 = 2 \).

Step4: Find \( BD \)

Substitute \( x = 2 \) into \( BD = 2x + 6 \): \( BD = 2(2) + 6 = 4 + 6 = 10 \).

Answer:

\( 10 \)