Question

Find the length of the tangents drawn from an external point to a circle of radius 5cm, if they are inclined to each other at an angle of 90degree.

Answer 1

the quadrilateral so formes is a square therefore the length of tangents are 5 cm each

Answer 2

Answer:

 

Step-by-step explanation:

For better explanation of the solution, see the attached figure of the problem :

Now, in quadrilateral ABCD

Since, the tangents are inclined to each other at 90°

⇒ ∠BCD = 90°

Also, tangents to the circle are perpendicular to the radius of the circle

⇒ ∠ADC = ∠ABC = 90°

So, By using angles sum property of a quadrilateral in ABCD

∠ABC + ∠BCD + ∠ADC + ∠BAD = 360°

⇒ 90 + 90 + 90 + ∠BAD = 360

⇒ ∠BAD = 90°

Now, all the angles of the quadrilateral ABCD is 90°

Also, adjacent sides AB and AD are equal as they are the radius of the same circle.

⇒ All the sides of the quadrilateral ABCD are equal.

Now, length of radius = 5 cm

⇒ BC = DC = 5 cm

Therefore, The length of tangents = 5 cm