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Answer :
No, PR is not the diameter of the circle. The given information and the measurements of the angles indicate that PR is simply a chord of the circle, but not the diameter.
To determine whether PR is the diameter of the circle, we need to consider the properties of a circle and the given information.
First, let's analyze the information provided:
PX = QX: This tells us that P and Q are equidistant from X, which means that PX and QX are radii of the circle.
SPX is 29 degrees: This angle is formed by the lines SP and PX.
QXP is 48 degrees: This angle is formed by the lines QX and XP.
XQP and XPQ are both 66 degrees: These angles are formed by the lines XQ and PQ.
RQX is 29 degrees: This angle is formed by the lines RQ and QX.
Now, let's examine the given information and its implications:
PX = QX implies that PXQ is an isosceles triangle, where PX and QX are equal radii of the circle. Therefore, angle XPQ is equal to angle XQP, both measuring 66 degrees.
If angle XPQ and angle XQP are both 66 degrees, then angle PXQ (inside the triangle) must be 180 - (66 + 66) = 48 degrees.
Since RQX is given as 29 degrees, angle PXQ (48 degrees) is larger than angle RQX (29 degrees), which means that PQ is longer than QR.
Based on the given information, PQ is longer than QR, so PQ cannot be the diameter of the circle. If PR were the diameter, PQ and QR would have equal lengths, but that is not the case.
In conclusion, PR is not the diameter of the circle.
Learn more about diameter at: brainly.com/question/31445584
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