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. ⇒ OQ2 + QP2 = OP2 ⇒ 202 + 212 = y2 ⇒ y2 = 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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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
Question : A circle of radius 5 cm and the length of tangent drawn from a point $X$ outside the circle is 12 cm. The distance of the point $X$ from the centre of the circle is:
Option 1: 12 cm
Option 2: 11 cm
Option 3: 10 cm
Option 4: 13 cm
Question : Find the length of a tangent drawn to a circle with a radius of 6 cm, from a point 10 cm from the centre of the circle.
Option 2: 9 cm
Option 3: 8 cm
Option 4: 10 cm
Question : Find the length of a tangent drawn to a circle with a radius 8 cm from a point 17 cm from the centre of the circle.
Option 1: 14 cm
Option 2: 12 cm
Option 3: 15 cm
Question : PX is a tangent drawn from point X, that touches the circle at P. O is the centre of the circle. The radius of this circle is 10 cm and OX = 26 cm. What is the length of PX?
Option 1: 24.5 cm
Option 2: 24 cm
Option 3: 23.5 cm
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