Math Problem Statement

Find ∠POR given that ∠PRQ = 33° in a cyclic quadrilateral.

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:

  1. The angle at point P (∠PRQ) is 33° as given.
  2. 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.
  3. The angle ∠POR subtended at the center by the same arc PR will thus be double of the angle ∠PRQ.

Formula:

POR=2×PRQ\angle POR = 2 \times \angle PRQ

Substitute the given value: POR=2×33=66\angle POR = 2 \times 33^\circ = 66^\circ

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