Arcs, Chords, and Inscribed Angles of Circles

Name Computer Number

I. Construct Circle P (Label the child). Construct a point on the circle, label as point T.

Choose point T and center P; construct "line". Choose this line and the circle; construct "point at intersection"; label as K.

Construct segment TK, hide line TK. TK should be a diameter.

Construct a point on the circle; label as A.

Choose point A and segment TK; construct "perpendicular line".

Choose this line and the circle; construct "point at intersection"; label as B.

Construct segment AB; hide line AB.

Choose segment TK and segment AB; construct "point at intersection"; label as R.

Construct segments AP and PB. (Make sure that point K is between the minor arc AB).

PRA = , therefore Triangle PRA is a triangle.

Using the Pythagorean Theorem, show that your conjecture about Triangle PRA is true.

PA = PB = PK = All three segments are

PR = RK =

What is the relationship between these two segments and PK?

AB = AR = RB = Arc AB = Arc AK = Arc KB =

In a circle, if a diameter is perpendicular to a chord, then it the chord and its arc.

Construct Circle C. Choose the circle and "measure" radius.

Move the circle using the child until the radius is equal to 4 cm.

Construct two chords (non-intersecting), label as PQ and RS.

Let PQ = 5 and RS = 5.

Arc PQ = Arc RS =

In circle, two minor arcs are if and only if their corresponding chords are congruent.

Construct the midpoints of segments PQ and RS. Label as M and N, respectively.

Construct the perpendicular bisector of segment PQ and RS. (Choose the midpoint and the segment, construct "perpendicular line".)

What can you conclude about the perpendicular bisectors of chords of a circle?

Construct segment MC; hide line MC.

Construct segment NC; hide line NC.

MC = NC = PQ = RS =

In a circle, two chords are if and only if they are from the center.

Make PQ and RS equal to 5, then 6, then 7. Does your conjecture hold true?

Define Inscribed Angle:

Construct Circle B. Construct three points on the circle, label as X, Y, and Z.

(Make sure Y is between points X and Z).

Construct chords XY and YZ.

Measure XYZ and move chords around until the angle is 65 degrees.

Measure Arc XZ = This is called the "intercepted arc".

If an angle is inscribed in a circle, then what can you conclude about the intercepted arc?

Make XYZ equal to 90 degrees. What can you conclude about its intercepted arc?

This arc is known as .

Make XYZ equal to 40 degrees. Construct a point, W in between points X and Y on the circle.

Construct segments WX and WZ.

XWZ = The intercepted arc for this angle is Arc and equals .

It two inscribed angles of a circle intercept the same arc, then the angles are .

Construct Circle A. Construct four points on the circle, P, Q, R, and S.

Construct segments PQ, QR, RS, and PS. This is called an "inscribed polygon".

Define Inscribed Polygon:

QPS = QRS = PQR = PSR =

If a quadrilateral is inscribed in a circle, then its opposite angles are .