Question

The length of the tangent drawn from a point 6 cm away from the centre of a circle with radius 3 cm is ......... cm​

Answer 1

• Given a tangent is drawn to a circle from a point 6 Cm away from the centre of the circle or radius = 3 cm

So ,let us first name those points so let the centre be O point away from the centr e from where the tangent is drawn is P and the intersection point of the tangent to the circumference of the circle is R ✓

Now, we know that the radius of a circle is perpendicular to the tangents drawn to its circumference so it makes 90 ° to it

So from all this above information we find this three points makes a ∆OPR

So in right angled triangle OPR ,we have the

$\red{hypotenuse = 6cm} \\ \\ \red{height = 3cm} \\ \\ \red{base = need \: to \: be \: calculate \:}$

So We can apply Pythagoras theorem to find the length of the tangent of the base of the ∆OPR

$\huge{Pythagoras \: theorem}$

$hypotenuse ^{2} \: = base ^{2} + height {2}$

$= > 6 ^{2} = 3 ^{2} + base ^{2} \\ \\ = > 36 = 9 + base ^{2} \\ \\ = > base = \sqrt{36 - 9} \\ \\ = > base = \sqrt{27} \\ \\ = > base = 5.1 \: cm$

So from the above calculation we find the length of the tangent is 5.1 cm That is also the base of the ∆OPR