1. a) \(O\) thuộc các đoạn thẳng: \(A B ; \&\text{nbsp}; C D ; \&\text{nbsp}; O A ; \&\text{nbsp}; O B ; \&\text{nbsp}; O C ; \&\text{nbsp}; O D .\)

b) Ta có \(O\) nằm giữa hai điểm \(A\) và \(B\) và \(O A \&\text{nbsp}; = \&\text{nbsp}; O B \&\text{nbsp}; = 3\) cm nên \(O\) là trung điểm của đoạn thẳng \(A B .\)

2. a) Số đo góc \(x O y\) bằng \(3 0^{\circ}\).

a) \(\frac{5}{17} - \frac{25}{31} + \frac{12}{17} + \frac{- 6}{31}\)

\(= \frac{5}{17} - \frac{25}{31} + \frac{12}{17} + \frac{- 6}{31}\)

\(= \left(\right. \frac{5}{17} + \frac{12}{17} \left.\right) + \left(\right. - \frac{25}{31} + \frac{- 6}{31} \left.\right)\)

\(= 1 + \left(\right. - 1 \left.\right)\)

\(= \&\text{nbsp}; 0\)

b) \(\frac{17}{8} : \left(\right. \frac{27}{8} + \frac{11}{4} \left.\right)\)

\(= \frac{17}{8} : \left(\right. \frac{27}{8} + \frac{22}{8} \left.\right)\)

\(= \frac{17}{8} : \frac{49}{8}\)

\(= \frac{17}{49}\).

c) \(\frac{1}{5} \cdot \frac{11}{16} + \frac{1}{5} \cdot \frac{5}{16} + \frac{4}{5}\)

\(= \frac{1}{5} \cdot \left(\right. \frac{11}{16} + \frac{5}{16} \left.\right) + \frac{4}{5}\)

\(= \frac{1}{5} \cdot 1 + \frac{4}{5}\)

\(= \frac{1}{5} + \frac{4}{5} = 1.\)

d) \(\frac{5}{6} : 25 - 2 + \frac{- 7}{3} \cdot \frac{2}{7}\)

\(= \frac{5}{6} : 25 - 2 + \frac{- 7}{3} \cdot \frac{2}{7}\)

\(= \frac{5}{6} \cdot \frac{1}{25} - 2 + \frac{- 2}{3}\)

\(= \frac{1}{30} - 2 + \frac{- 2}{3}\)

\(= \frac{1}{30} - \frac{60}{30} + \frac{- 20}{30}\)

\(= \frac{1}{30} - \frac{60}{30} + \frac{- 20}{30} = \frac{- 79}{30}\)