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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