Question

a is equidistant to b and c. find bd. bd = ? b 12x - 8 d 8x + 8 c

Explanation:

Step1: Recognize the triangle property

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

$$ 12x - 8 = 8x + 8 $$

Step2: Solve for \( x \)

Subtract \( 8x \) from both sides:

$$ 12x - 8x - 8 = 8 $$

$$ 4x - 8 = 8 $$

Add 8 to both sides:

$$ 4x = 8 + 8 $$

$$ 4x = 16 $$

Divide by 4:

$$ x = \frac{16}{4} = 4 $$

Step3: Find \( BD \)

Substitute \( x = 4 \) into \( BD = 12x - 8 \):

$$ BD = 12(4) - 8 $$

$$ BD = 48 - 8 $$

$$ BD = 40 $$

Answer:

\( 40 \)