Question

3) O is the center of the circle. Assume that lines that appear to be tangent are tangent. What is the value of x?

Answer 1

Answer: The value of x = 48°.

Explanation:

Since we have given that

O is the center of the circle and PA and PB are two tangents.

Angle at the center = ∠AOB = 132°

We need to find the value of x .

Since Radius forms right angle at the tangents as it is the shortest distance from the center to the tangent.

So, ∠PAO= 90°

∠PBO = 90°

since it forms a quadrilateral,

So, we know that " Sum of all angles in the quadrilateral is 360°. "

So, we have

`\angle P+\angle PAO+\angle PBO+\angle AOB=360\textdegree\\\\x+90\textdegree+90\textdegree+132\textdegree=360\textdegree\\\\x+312\textdegree=360\textdegree\\\\x=360\textdegree-312\textdegree\\\\x=48\textdegree`

Hence, the value of x = 48°.

Answer 2

We know that the angles of a quadrilateral add to a 360° angle.
And there is two right angles at the point of the tangent.
We deduce the equation:
x+90+90+132=360
then
x=360-90-90-132=48.
Answer x=48.