Question

a is equidistant to b and c. find bd. bd = ? b 3x + 5 d 7x - 3 c

Explanation:

Step1: Identify the property

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

Step2: Set up the equation

Set \( 3x + 5 = 7x - 3 \).

Step3: Solve for \( x \)

Subtract \( 3x \) from both sides: \( 5 = 4x - 3 \).
Add 3 to both sides: \( 8 = 4x \).
Divide by 4: \( x = 2 \).

Step4: Find \( BD \)

Substitute \( x = 2 \) into \( BD = 3x + 5 \): \( BD = 3(2) + 5 = 6 + 5 = 11 \).

Answer:

11