Question
Download Solution PDFThe 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.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A circle with center O and AB is the tangent from point A.
Radius of circle = OB = 5cm
Distance of point from the circle = 10cm
Concept used:
Tangent of any circle is perpendicular to the radius of a circle.
Pythagoras theorem:
(Base)2 × (Perpendicular)2 = (Hypotenuse)2
Calculation:
Since, AB is tangent.
Therefore,
Using Pythagoras theorem in triangle OAB.
AO2= AB2 + OB2
(10)2= AB2+ (5)2
100 = AB2+ 25
75 = AB2
\(5{\sqrt{3}}\) = AB
Hence, the length of a tangent drawn to this circle from a point at a distance of 10 cm from its centre is \(5{\sqrt{3}}\) cm.
Last updated on Jul 17, 2025
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