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
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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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Question : A tangent is drawn from a point M to a circle, which meets the circle at T such that MT = 12 cm. A secant MAB intersects the circle at points A and B. If MA = 8 cm, what is the length (in cm) of the chord AB?
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Question : Two concentric circles are drawn with radii of 20 cm and 16 cm. What will be the length of a chord of the larger circle which is tangent to the smaller circle?
Question : In the given figure, PAB is a secant and PT is a tangent to the circle from P. If PT = 8 cm, PA = 6 cm, and AB = $x$ cm, then the value of $x$ is:
Question : In the figure, $\mathrm{XYZ}$ is a secant and $\mathrm{ZT}$ is a tangent to the circle at $\mathrm{T}$. If $\mathrm{TZ}=12$ $\mathrm{cm}$ and $Y Z=8 \mathrm{~cm}$, then find the length of $XY$.
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