Question : A tangent AB at point A of a circle of radius 6 cm meets a line through the centre O at point B. If OB = 10 cm, then the length of AB (in cm) is equal to:
Option 1: 5
Option 2: 6
Option 3: 4
Option 4: 8
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Correct Answer: 8
Solution : Given, AB is a tangent, OB = 10 cm and OA = 6 cm Since tangent is perpendicular to the radius at its point of contact, $\angle$OAB = 90$^\circ$ Using Pythagoras theorem, OB2 = AB2 + OA2 ⇒ 102 = AB2 + 62 ⇒ AB2 = 64 ⇒ AB = 8 cm Hence, the correct answer is 8.
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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 1: 12 cm
Option 2: 9 cm
Option 3: 8 cm
Option 4: 10 cm
Question : The radius of a circle is 3 cm and 'O' is its centre. The length of the tangent (in cm) to the circle drawn from a point P, which is at a distance of 5 cm from 'O' is:
Option 1: 4
Option 3: 5
Option 4: 3
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 : In a circle with a centre at O(0,0) and a radius of 5 cm, AB is a chord of length 8 cm. If OM is perpendicular to AB, then the length of OM is:
Option 1: 2.5 cm
Option 2: 3 cm
Option 3: 4 cm
Option 4: 1 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
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