what will be the length of the tangent from apoint at a distance of 8cm radius of circle is 5.
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what will be the length of the tangent from apoint at a distance of 8cm radius of circle is 5.
Given:- A circle with center O and AB is the tangent from point A.
Radius of circle =OB=8cm
Distance of point from the circle =AO=10cm
To find:- Length of tangent, i.e., AB=?
Solution:-
Since AB is tangent,
Therefore,
AB⊥OB[∵Tangent at any point of circle is perpendicular to the radius through point of contact]
⇒∠ABO=90°
Hence △OAB is a right angle triangle.
Using pythagoras theorem in △OAB,
AO2=AB2+OB2
(10)2=AB2+(8)2
⇒AB=100−64=6cm
Hence the length of tangent is 6cm.
Hence the correct answer is 6cm
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