QR is a diameter of a circle,centre O,and P is a point on its circumference.
Given that PQR= 25°, calculate
a, POR
b, OPR
c, the value, correct to 2 significant figures of PQ/QR.
1
Expert's answer
2020-07-19T15:54:05-0400
Consider the circle with center O and the diameter PQ
centralangle=interceptedarc
The measure of each inscribed angle is exactly half the measure of its intercepted arc.
In a circle, the measure of an inscribed angle is half the measure of the central angle with the same intercepted arc.
a. The angle ∠PQR is an inscribed angle
m∠PQR=21mPR
The angle ∠POR is a central angle
m∠POR=mPR=2m∠PQR=2⋅25°=50°
b. We see that OP and OR are radii of the circle. Then ΔPOR is the equilateral triangle
OP=OR,m∠OPR=m∠ORP
The three interior angles in a triangle will always add up to 180°
m∠OPR+m∠ORP+m∠POR=180°
m∠OPR+m∠ORP=180°−m∠POR
m∠OPR=2180°−m∠POR
m∠OPR=2180°−50°=65°
c. An angle inscribed in a semicircle is a right angle. Then
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