# 1996COMC加拿大数学公开赛真题免费下载

### 1996 COMC真题免费下载

Part A共10题，每题3分

Part B共3题，每题10分

#### 部分真题预览：

Part A :

3)The vertices of a right-angled triangle are on a circle of radius R and the sides of the triangle are tangent to another circle of radius r. If the lengths of the sides about the right angle are 16 and 30, determine the value of R+r.

5)A road map of Grid City is shown in the diagram. The perimeter of the park is a road but there is no road through the park. How many different shortest road routes are there from point A to point B?

6)In a 14 team baseball league, each team played each of the other teams 10 times. At the end of the season, the number of games won by each team differed from those won by the team that immediately followed it by the same amount. Determine the greatest number of games the last place team could have won,assuming that no ties were allowed.

Part B :

1)Three numbers form an arithmetic sequence, the common difference being 11. If the first number is decreased by 6, the second is decreased by 1 and the third is double, the resulting numbers are in geometric sequence. Determine the numbers which form the arithmetic sequence.