JAMB - Mathematics (1999 - No. 35)
In the figure above, TZ is tangent to the circle QPZ. Find x if TZ = 6 units and PQ = 9 units
3
4
5
6
Vysvetlenie
The Tangent Theorem states that if a tangent line is drawn to a circle from an external point, then the square of the length of the tangent segment is equal to the product of the lengths of the entire secant segment and its external part. If P is an external point, AAA is the point of tangency, and B and C are points where the secant intersects the circle, the theorem can be expressed as: (PA)\(^2\) = PB . PC
(ZT)\(^2\) = PT.QT
6\(^2\) = x(9 + x)
x\(^2\) + 9x - 36 = 0
(x + 12)(x - 3) = 0
x = - 12 or 3