Question

find the value of ( x ). note that ( ac = 15 ), ( bc = x ), ( cd = 5 ), and ( ce = 12 ).

Explanation:

Step1: Apply Secant-Secant Power Theorem

For point \(C\) outside the circle, the theorem states \(CA \times CB = CE \times CD\)

Step2: Substitute given values

Substitute \(AC=15\), \(BC=x\), \(CE=12\), \(CD=5\):
\(15 \times x = 12 \times 5\)

Step3: Simplify and solve for \(x\)

Calculate right-hand side: \(12 \times 5 = 60\), then solve:
\(x = \frac{60}{15}\)

Answer:

\(4\)