Check Your Understanding
A. In Circle O, AD ≅ BC,
1. If mAD = 60°, what is mBC?
2. If m ∠AOD = 85°, what is m∠ BOC?
3. If m∠AOD = 75°, what is mBC?
4. If mBC = 60°, what is m∠AOD?
O
D C
A B
• A circle is the set of points in a plane that are at the same distance from
a given point in the plane called the center.
• The segment from the center to any point of the circle is called the radius.
• A segment whose endpoints lie on the circle is called the chord.
• A chord that passes through the center is called the diameter.
• A secant is a line that intersects the circle in two points.
• A tangent line is coplanar with the circle and intersects the circle in
exactly one point.
• A central angle is an angle whose vertex is in the center of the circle.
• An inscribed angle is an angle formed when two secant lines intersect.
Its vertex lies on the circle and its sides are chords of the circle.
• The semicircle is half of a circle. It is the union of the endpoints of a
diameter and all points on the circle that lie on one side of the diameter.
Its degree measure is 180°.
• The minor arc is an arc smaller than a semicircle.
• The major arc is an arc larger than a semicircle.
• If a radius is perpendicular to a chord, then it bisects the chord.
• The measure of a central angle is equal to the measure of its intercepted
arc.
• The measure of an inscribed angle is one-half the measure of its
intercepted arc.
• The measure of an arc formed by two adjacent, non-overlapping arcs is
the sum of the measures of the two arcs.
Page 8 of 9
MATH 7 QUARTER 3 WEEK 7
Refer to the diagram below to solve the items in B and C.
B. Given radius OR ⊥ chord AB at C,
AC = 2x – 6, BC = x + 8
5-7) Find: AC, BC, and AB
C. Given OR ⊥ chord AB at C
AC = 4x + 10, BC = 7x – 5
8-10) Find: AC, BC, and AB.
(nonsense report answer/account) i will give 30 points
Answer:
A.
1. 31
2. (8× + 10) and (4× – 15)
3. 75°
4. 60°
B.
5-7. to find AC
cos (60°) = AC/12
to find BC
sin (60°) = BC/12
C.
8-10.
AC = 2(x – 3) = 2(14-3) = 22
BC = x + 8= 14 + 8 = 22
AB = AC + AB = 22 + 22 = 44
Step-by-step explanation:
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