Sally drew a circle with right triangle PRQ inscribed in it, as shown below: The figure shows a circle with points P, Q, and R o
n it forming an inscribed triangle. Side PQ is a chord through the center and angle R is a right angle. Arc QR measures 40 degrees. If the measure of arc QR is 40°, what is the measure of angle PQR? 20° 40° 50° 70°
Side PQ is a chord through the center and angle R is a right angle. This means that side PQ is the diameter of the circle.
Let O represent the center of the circle.
If the measure of arc QR is 40°, it means that the central angle formed by arc QR is 40°. Side OR and side OQ are equal because they are both radius of the circle. Therefore, ∆QOR is an isosceles triangle and the base angles are equal.
Therefore, ∠PQR = ∠ORQ
Since the sum of the angles in a triangle is 180°, then
The greatest common factor is a^2. It cannot be 3ab or 3a^2b because b is not present in the last term (a^2). Similarly there is no 3 or multiple of 3 in a^2.
