Question : Tangent drawn from a point Y touches the circle at X, O is the centre of this circle. If OY = 50 cm and XY = 40 cm, then what will be the radius of this circle?
Option 1: 60 cm
Option 2: 75 cm
Option 3: 45 cm
Option 4: 30 cm
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Correct Answer: 30 cm
Solution : Given: OY = 50 cm and XY = 40 cm Use the Pythagorean theorem to find the length of OX, which is the radius of the circle [in $\triangle OXY$] OY2 = OX2 + XY2 ⇒ OX2 = OY2 – XY2 ⇒ OX2 = (50)2 – (40)2 ⇒ OX2 = 2500 – 1600 = 900 ⇒ OX = $\sqrt{900}$ = 30 cm Hence, the correct answer is 30 cm.
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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
Option 4: 25 cm
Question : Tangent drawn from point X touches the circle at U. O is the centre of this circle. If XU = 15 cm and OU = 8 cm, then what is the value of OX?
Option 1: 12 cm
Option 2: 19 cm
Option 3: 21 cm
Option 4: 17 cm
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 2: 11 cm
Option 3: 10 cm
Option 4: 13 cm
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
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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