Question : DE is a chord and KDE is a secant of a circle. If KD = 9 cm, DE = 7 cm and KH is a tangent to the circle at point H, find KH.
Option 1: 12 cm
Option 2: 25 cm
Option 3: 16 cm
Option 4: 144 cm
Correct Answer: 12 cm
Solution :
Suppose a tangent segment and a secant segment are drawn to a circle from an exterior point. In that case, the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.
$KH^{2} = KD \times KE$
$⇒KH^{2} = 9 \times 16 = 144$ cm
$\therefore KH = 12$ cm
Hence, the correct answer is 12 cm.
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