Question

in each of the following, O is the center of the circle.find the size of each lettered angle
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Answer 1

Answer:

egg

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Solution:-

Given that

O is the centre of the circle

Let P be the exterior point

PA is the tangent

The angle between the radius of the circle and the tangent at the point of contact is 90°

angle BAP = 90°

So, ∆ BAP is a right angled triangle

Given that

BA and AP are equal

=> angle APB = angle ABP

Since the angles opposite to equal sides are equal.

x = y

We know that

The sum of all angles in a triangle is 180°

=> angle BAP+angle APB+angle ABP

=> 90°+x+y = 180°

=> 90°+x+x = 180°

=> 90°+2x = 180°

=> 2x = 180°-90°

=>2x = 90°

=>x = 90°/2

=>x = 45°

=>y = 45°

Therefore, x = y = 45°

Answer:-

1) x = 45°and y = 45°

Used formulae:-

The angle between the radius of the circle and the tangent at the point of contact is 90°