Question no. viii). In the given figure, O is centre of the circle. Find the value of x and y? This is my last question.

•x = 45° and

•y = 45°

Step-by-step explanation:

Given,

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°

⇛∠BAP+∠APB+∠ABP

Substitute the value in equation then, we get

⇛90°+x+y = 180°

⇛90°+x+x = 180°

⇛90°+2x = 180°

⇛2x = 180°-90°

⇛2x = 90°

⇛x = 90°/2

⇛x = 45°

⇛y = 45°

.°. x = y = 45°

Answer: Hence, the value of x = 45° and y = 45°.

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

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Since the transformation occurring is rotation at 180 degrees about the origin, then the resulting image would be a reflection of the original image. Additionally, since the rotation is 180 degrees, then there is a movement of 2 quadrants for the corners A, B and C.

Therefore this would also mean that if point A is in coordinate (x, y) then point A’ would be in coordinate (-x, -y). Similar is true with point B and point C and their corresponding reflection corners point B’ and point C’. So for example if point A is located at (-5, 3) then point A’ must be at (5, -3).