Question

Find the value of x.

B
С
2
Х
30°
A
30
5
D
5
x = [?]

Answer 1

CD = 2 = x

Explanation:

Remark

The problem is not in getting x. The answer is 2. The problem is showing y.

Givens

Call the center of the circle O.

BO,AO,CO,DO circle radii

Chords AB and CD

AB = 2

<BOA = <COD

Solution

BO,AO,CO,DO area all equal to each other. All are radii.

<BOA = <COD = 30 Given

ΔBOA = ΔCOD SAS

AB = CD CPCTC

CPCTC means corresponding parts of Congruent Triangles are congruent.

Note also that AB and CD must be chords.