Question

central angles. in circle a, ∠bae = ∠dae. what is the length of be? 34 units, 27 units, 14 units, 17 units. 3x - 24, x + 10

Explanation:

Step1: Use the property of equal - central angles

Since \(\angle BAD=\angle DAE\) in circle \(A\), then the chords \(BD\) and \(DE\) are equal. So we set up the equation \(3x - 24=x + 10\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(3x-x-24=x - x+ 10\), which simplifies to \(2x-24 = 10\). Then add 24 to both sides: \(2x-24 + 24=10 + 24\), getting \(2x=34\). Divide both sides by 2: \(x = 17\).

Step3: Find the length of \(DE\)

Substitute \(x = 17\) into the expression for \(DE\) which is \(x + 10\). So \(DE=17 + 10=27\).

Answer:

27 units