Question : The radius of a circle is 5 cm. Calculate the length of a tangent drawn to this circle from a point at a distance of 10 cm from its centre.
Option 1: $5 \sqrt{5}$ cm
Option 2: $5 \sqrt{2}$ cm
Option 3: $5$ cm
Option 4: $5 \sqrt{3}$ cm
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Correct Answer: $5 \sqrt{3}$ cm
Solution : In $\triangle OAB$, $AO^2 = AB^2 + OB^2$ ⇒ $10^2 = AB^2 + 5^2$ ⇒ $100 = AB^2 + 25$ ⇒ $75 = AB^2$ ⇒ $AB = 5\sqrt3$ Hence, the correct answer is $5\sqrt3$ cm.
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Question : The radius of a circle is 6 cm. The distance of a point lying outside the circle from the centre is 10 cm. The length of the tangent drawn from the outside point to the circle is:
Question : Two circles touch each other externally. The radius of the first circle with centre O is 6 cm. The radius of the second circle with centre P is 3 cm. Find the length of their common tangent AB.
Question : A secant PAB is drawn from an external point P to the circle with centre O, intersecting it at A and B. If OP = 17 cm, PA = 12 cm, and PB = 22.5 cm, then the radius of the circle is:
Question : Let O be the centre of the circle and P be a point outside the circle. If PAB is a secant of the circle which cuts the circle at A and B and PT is the tangent drawn from P, then find the length of PT, if PA = 3 cm and AB = 9 cm.
Question : Point O is the centre of a circle of radius 5 cm. At a distance of 13 cm from O, point P is taken. From this point, two tangents, PQ and PR, are drawn to the circle. Then, the area of quadrilateral PQOR is:
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