in circle a, ∠bae ≅ ∠dae. what is the length of (overline{be})? 14 units 17 units 27 units 34 units
in circle a, ∠bae ≅ ∠dae. what is the length of (overline{be})? 14 units 17 units 27 units 34 units
Answer
Explanation:
Step1: Use congruent - angle property in circle
In a circle, if $\angle BAE\cong\angle DAE$, then the chords opposite these angles are equal. So, $BE = DE$. That means $3x - 24=x + 10$.
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 $BE$
Substitute $x = 17$ into the expression for $BE$ (we can use either $BE=3x - 24$ or $BE=x + 10$). Using $BE=x + 10$, we have $BE=17 + 10=27$.
Answer:
27 units