Question : In a circle with a radius of 20 cm, X is a point located at a distance of 29 cm from the centre of the circle. What will be the length (in cm) of a tangent drawn from point X to the circle?
Option 1: 23
Option 2: 20
Option 3: 21
Option 4: 18
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Correct Answer: 21
Solution :
We know the theorem states that the tangent is perpendicular to the radius of a circle$(\angle T=90^{\circ})$.
Let,
$OT=20\text{ cm}$
$OX=29\text{ cm}$
In $\triangle OTX$
According to the Pythagoras' theorem,
$OX^2 = OT^2 + TX^2$
⇒ $TX = \sqrt{OX^2 - OT^2} = \sqrt{(29)^2 - (20)^2} = \sqrt{441} = 21 \text{ cm}$
Hence, the correct answer is 21.
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