Question

Help me out please? Math photo

Answer 1

Answer: (20) x = 8 , (21) x = 4√3  , (22) x = 9  , (23) x = 2√3  , (24) x = 140°  , (25) x = 82°

Step-by-step 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) $\frac{1}{2}$(outside arc - inside arc) = vertex angle

     $\frac{1}{2}$(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