Circles - Angle Measurement from Intersection & Segment Measurements
Lesson: ​Geometry
1) In the figure on the right, ​∠C, the central angle, measures 38°. What is the
measurement of θ?
a.
19​°
b.
38​°
c.
57​°
d.
76​°
2) In the figure on the right, line AB is tangent to the circle at point B. If ∠CAB
measures 15°, what is the measurement of
∠BCA?
a.
55​°
b.
65​°
c.
75​°
d.
85​°
3) In the figure on the right, two lines are tangents to a circle at points A and B. If
︿
mADB measures 270​°, what is the value of ​θ?
a.
22.5​°
b.
45​°
c.
55°
d.
90°
4) In the figure on the right, two chords lie inside the circle. Find the value of θ.
a.
18​°
b.
38​°
c.
142​°
d.
162​°
5) In the figure below, A, B, C, and D are points on the circle. If ∠ADB measures 25​°​,
what must be the measure of ∠ACB?
a.
12.5​°
b.
25​°
c.
37.5​°
d.
50​°
6) Given that DE measures 12 units, CD measures 3 units, and CB measures 5
units, find the ratio of AB to DE .
a.
1:3
b.
3:1
c.
3:5
d.
5:3
7) Given that CD and AB are 12 and 18 units long respectively in the figure to the
right, determine the length of BC .
a.
3 units long
b.
6 units long
c.
12 units long
d.
24 units long
8) Let I be the intersection of AB and CD. Given that B I = 2x + 8 , C I = x + 7 , AI = 5 ,
and DI = 7 , find the value of x.
a.
2
b.
3
c.
4
d.
5
9) Given that a 16 cm chord of a circle lies 15 cm away from its center, find the
diameter of the circle.
a.
17cm
b.
20cm
c.
34cm
d.
40cm
10) A circle is inscribed in an equilateral triangle ABC with D, E, and F as the points of
tangency. Given that AB = AC, BC = 12, and BD:AD = 2:1, find the length of the
radius of the circle.
a.
2√3 cm
b.
3√3
3
cm
c.
4√3
3
cm
d.
6√3 cm
11) Three circles of radius 2cm, 3cm, and 10cm are externally tangent to each other.
Find the area of the triangle formed by the centers of the circles.
a.
30 units
b.
45 units
c.
60 units
d.
65 units
12) Two circles of radii 9cm and 1cm, are joined by a common external tangent of
length 17cm. Find the distance between their
centers.
a.
9cm
b.
10cm
c.
15cm
d.
17cm
13) A point B outside the circle O is 25 cm from the center of the circle. If BD, a
tangent to the circle at point D, measures 24 cm, find the diameter of the circle.
a.
7cm
b.
12cm
c.
14cm
d.
24cm
14) A right triangle is inscribed in a circle of radius 10cm. What is the measure of its
hypotenuse?
a.
10cm
b.
15cm
c.
20cm
d.
25cm
15) In the figure on the right, A and B are centers of the circle of radii 3 cm and 6cm
respectively. If the two circles are joined by a common external tangent CD 40 cm
long, find AB or the distance between the
center of the 2 circles.
a.
41cm
b.
45cm
c.
49cm
d.
52cm