Question : In a circle with a radius 20 cm, P is a point located at a distance of y cm from the centre of the circle. If the length of a tangent drawn from point P to the circle is 21 cm, find the value of y.
Option 1: 31 cm
Option 2: 28 cm
Option 3: 29 cm
Option 4: 25 cm
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Correct Answer: 29 cm
Solution :
Given that OP = y cm, QP = 21 cm, OQ = 20 cm.
To find the length of OP, apply Pythagoras theorem in $\triangle$OPQ.
⇒ OQ
2
+ QP
2
= OP
2
⇒ 20
2
+ 21
2
= y
2
⇒ y
2
= 400 + 441 = 841 cm
⇒ OP = $\sqrt{841}$ = 29 cm
Thus, the length of the point from the centre of the circle is 29 cm.
Hence, the correct answer is 29 cm.
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