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

Question

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

Team Careers360 · Accepted Answer

Correct Answer: $5 \sqrt{3}$ cm

Solution :
In $ riangle 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 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: 55 cmOption 2: 52 cmOption 3: 5 cmOption 4: 53 cm

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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