Review Ch. 10. Complete all problems on a separate sheet of paper. Be sure to number each problem. Good Luck!. Problem #1. Find the exact length of arc AB, if circle P has a radius of 18cm. A. P. 100 °. B. Solution to #1. Arc Length = (100/360) * 36 π
Complete all problems on a separate sheet of paper.
Be sure to number each problem. Good Luck!
Find the exactlength of arc AB, if circle
P has a radius of 18cm.
Arc Length = (100/360) * 36π
= (5/18) * 36π
= 10π cm.
Find the diameter of a circle in which a 36 cm chord is 80 cm from the center.
This is a 9, 40, 41 triangle times 2 so r = 82cm diameter = 164 cm.
Find the radius of a circle with a circumference of
Circumference = π * diameter so the
diameter must be 20 so radius = 10.
Find the measure of arc AE.
*Arc BC = 360 – 210 = 150о
*Angle BDC is supp (tangent-tangent) = 30о
*So Angle ADE = 30о
*So 30 = (1/2)(200 – x)
60 = 200 – x
x = 140о
In the circumscribed polygon, find the length of the AB.
AB = 15 – (10 – x) + 12 – x
= 5 + x + 12 – x
In circle O, AB is a diameter.
OA=3x+5 and OB=2(5x-1).
OA and OB are both radii so are equal.
3x + 5 = 2(5x – 1)
3x + 5 = 10x – 2
7 = 7x
1 = x
each radius = 8 ; so diameter AB = 16
Solve for x if
Since angle A is inscribed;
2(5x + 6) = 12x – 2
10x + 12 = 12x – 2
14 = 2x
x = 7
MATH is inscribed in the circle.
Angle M has a measure of 78 degrees.
Find the measure of angle T.
Opp. Angles of inscribed quadrilaterals are
Measure of Angle T = 180 – 78 = 102о
Find the radius of the circle if AB is a diameter, , and BC=20.
*Measure of Angle B = 120/2 = 60
*Measure of Angle C = 90
*30 – 60 – 90 triangle with x = 20 ; so
diameter is 2x = 40
*Radius of AB is 20.
A circle is inscribed in triangle ABC. AB=14, AC=12 and BC=4. Find BD.
14 – x + 12 – x = 4
26 – 2x = 4
22 = 2x
x = 11
So BD = 14 – x = 3
A circle has a radius of 50. How far from the center is a chord of length 28?
7, 24, 25 right triangle
So x = 2 * 24 = 48
A regular octagon is inscribed in a circle.
What is the measure of an arc cut off by a side of the octagon?
* Regular - so all chords congruent.
* Congruent chords = congruent
360/8 = 45о
Two concentric circles have radii of lengths 16 and 20. Find the length of a chord of the larger circle that is tangent to the smaller circle.
x = 12 so length of the chord
A 12 by 10 rectangle is inscribed in a circle. Find the radius.
244 = c2
Two secants drawn to a circle from an external point intercept arcs that are 122° and 68°. Find the measure of the secant-secant angle.
= 82 π cm
A central angle intercepts an arc that is 5/12 of the circle. Find the measure of angle x.
of circle O
If PA and PB are tangent to circle O at A
and B, PA=24, and PO=26, find
perimeter of quadrilateral PAOB.
Find the measure of angle x.
What is the length of a chord that cuts off an arc of 120 degrees in a circle with a radius of 8?
Parallelogram ABCD is inscribed in circle Q, with dimensions of 24 by 10. Find the area of circle Q.
Circle A has a radius of 5 inches, and circle B has a radius of 20 inches. The centers are 39 inches apart. Find the length of the common external tangent (CD).
Two tangent segments of a circle with a diameter of 50 inches form a 60 degree angle where they meet at P. How far is P from the center of the circle?
AB & AC are tangent to the circle.
Find the measure of arc BDC.