Q. 14.7( 3 Votes )

From a point P, the length of the tangent to a circle is 15 cm, and the distance of P from the centre of the circle is 17cm. Then what is the radius of the circle?

Answer :

Let the centre of circle be O so that PO = 17 cm


Tangent is PB whose length is 15 cm


OB is radius as shown



Now we know that radius is perpendicular to point of contact


Hence OB is perpendicular to PB


Hence PBO = 90°


Consider ΔPBO


Using Pythagoras theorem


PB2 + OB2 = PO2


152 + OB2 = 172


OB2 = 172 - 152


OB2 = 289 – 225


OB2 = 64


OB = ±8


As length cannot be negative


OB = 8 cm


Hence length of radius is 8 cm


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