Answer: (20) x = 8 , (21) x = 4√3 , (22) x = 9 , (23) x = 2√3 , (24) x = 140° , (25) x = 82°
Explanation:
20) Given two intersecting chords inside a circle, the product of their segments is equal.
5 * x = 4 * 10
5x = 40
x = 8
21) Given a secant and a tangent line, the product of the outside segment and the entire segment length equals the square of the tangent segment.
4 * (8 + 4) = x²
4 (12) = x²
48 = x²
√48 = √x²
4√3 = x
22) Given two secant lines, the product of their outside segments and the entire segment lengths are equal.
4 * (5 + 4) = 3 * (3 + x)
4(9) = 3(3 + x)
4(3) = 3 + x
12 = 3 + x
9 = x
(23) Given two intersecting chords inside a circle, the product of their segments is equal.
6 * 2 = x * x
12 = x²
√12 = √x²
2√3 = x
24)
(outside arc - inside arc) = vertex angle
(30 - inside arc) = 10
30 - inside arc = 20
- inside arc = -10
inside arc = 10
outside arc + x + inside arc = 180 because they form a semi circle
30 + x + 10 = 180
40 + x = 180
x = 140
25) opposite angles of a quadrilateral inscribed in a circle are supplementary
98 + x = 180
x = 82