Your Turn: 9. Place the steps, given below, in the appropriate order to construct the inscribed equilateral triangle in a circle. a. Continue making consecutive arcs around the circle as described in step 3 until the circle has been divided into six 60° arcs. b. Using this radius, place the point of the compass at the endpoint of the radius on the circle and make an arc that intersects the circle. c. Construct the sides of the equilateral triangle by connecting the endpoints of three consecutive 120° arcs. d. Use the given center and the straightedge to construct a radius of the circle. Use the compass to measure the radius. e. Keeping the same radius, place the point of the compass at the point of intersection of the arc (from step 2) and make another arc that intersects the circle. Step 1 Step 2 Step 3 Step 4 Step 5 - --

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Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.