Math Problem Statement
Solution
The image you provided shows a circle with a triangle inscribed in it, with points labeled P, Q, R, and O. You are asked to find the angle ∠POR.
The angle ∠POR can be calculated using the properties of a cyclic quadrilateral or inscribed angles in a circle. Here's how to approach it:
Steps:
- The angle at point P (∠PRQ) is 33° as given.
- The inscribed angle theorem tells us that the angle subtended by an arc at the center of the circle is twice the inscribed angle subtended by the same arc.
- The angle ∠POR subtended at the center by the same arc PR will thus be double of the angle ∠PRQ.
Formula:
Substitute the given value:
So, the angle ∠POR is 66°.
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Math Problem Analysis
Mathematical Concepts
Circle Geometry
Inscribed Angles
Central Angles
Formulas
Central Angle = 2 × Inscribed Angle
Theorems
Inscribed Angle Theorem
Suitable Grade Level
Grades 8-10
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