From an external point P to a circle, a tangent PT and a secant PQR are drawn such that PT=10 cm, PQ=6 cm, and QR=x cm. Given that point Q lies between points P and R, find the value of x such that the secant intersects the circle at points Q and R.
Show answer & explanation
Correct answer: B
Explanation
Given:
PT = 10 cm
PQ = 6 cm
QR = x cm
PR = PQ + QR
By the formula:
PT² = PQ × PR
PR = 6 + x
10² = 6(6 + x)
100 = 36 + 6x
6x = 64
x = 64/6 = 10.67 cm