Question

Find the length of a tangent drawn to a circle with eadius 5cm,from a point 13cm from the centre of a circle

Answer 1

According to the problem given ,

radius = OP = 5 cm,

OA = 13 cm

Length of the tangent = AP

We know that ,

OP is perpendicular to AP

[ tangent , radius relation ]

Now ,

In ∆APO , <APO = 90°,

By Phythogarian theorem ,

OA² = AP² + OP²

=> 13² = AP² + 5²

=> 169 - 25 = AP²

=> 144 = AP²

=> 12² = AP²

=> AP = 12 cm

Therefore ,

length of the tangent = AP = 12 cm

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Answer 2

Heya mate,Here is ur answer

Given : Radius = 5 cm

Distance of point from center= 13 cm

We know that the tangent and the radius.ake an angle of 90° with each other.

So, using Pythagoras theorem that states that the sum of squares of other two sides in a right angled triangle gives the square of the hypotenuse.

So,

Hypotenuse ^2= base ^2 + perpendicular^2

Distance of point from center^2 = radius ^2 + tangent^2

13^2 =5^2 +Tangent^2

169=25 +Tangent^2

169-25=Tangent^2

144=Tangent ^2

√144=Tangent

12 = Tangent

$<b><u>So, the length of the tangent=12 cm.</u></b>$

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@Laughterqueen

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