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?

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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