Question

if the angle between two radii of a circle is 90 degrees then the angle between tangent drawn at the end of the radii is​

Answer 1

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Answer 2

Given,

The radii are perpendicular to each other.

To find,

The angle between tangent drawn at the end of the radii.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Here, the tangents (DX and DY) and radii (AB and BC) and forms a polygon with four sides (ABCD). In this polygon, the four angles are -

1) Angle ABC between two radii = 90° (given)

2) Angle BAD between first radius and it's tangent = 90° (As, angle between any radius and it's tangent is always 90°)

3) Angle BCD between second radius and it's tangent = 90°  (As, angle between any radius and it's tangent is always 90°)

4) Angle ADC between the two tangents = Let, x°

Now, in case of any four sided polygon, the sum of the four internal angles is always 360°.

So,

x+90+90+90 = 360

x+270 = 360

x = 360-270

x = 90

The fourth angle of that four sided polygon or the angle between the tangents (Angle ADC) = 90°

Hence, the angle between those two tangents are 90°