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O is the centre of a circle of radius 8 cm. The tangent at a point A on the circle cuts a line through O at B such that $AB = 15\ cm$. Find OB.
Given:
O is the centre of a circle of radius 8 cm. The tangent at a point A on the circle cuts a line through O at B such that $AB = 15\ cm$.
To do:
We have to find the length of OB.
Solution:
Radius $OA = 8\ cm$.
$AB = 15\ cm$
Let $XY$ be the tangent to the circle at $A$.
$OA\ perp\ XY$
In right angled triangle $OAB$,
By Pythagoras theorem,
$OB^2= OA^2+ AB^2$
$OB^2 = 8^2 + 15^2$
$= 64 + 225$
$= 289$
$= 17^2$
Therefore,
$OB = 17\ cm$
The length of OB is 17 cm.
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