Answer:
•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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