Here are some math problems to solve. These are questions which more are more or less like Olympiad type. Achievement of GCE 'O' level is sufficient to answer them but hey, they are intriguing. Figure them and enjoy.
1. Calculate the distance between a pair of opposite sides of a regular hexagon with sides 12 cm long.
2. Calculate, in cm correct to 2 decima places, the radius of the circumcircle of an isosceles triangle with sides of length 13 cm, 13 cm, 10 cm.
3. A chord 8.4 cm long is 5.2 cm from the centre of a circle. Calculate the radius of the circle
4. Two equal circles intersect, and the length of their common chord is 5.6 cm. If the centres of the circles are 9 cm apart, calculate their radii.
5. A batsman had scored 340 runs after a certain number of innings. In his next two innings he made 6 (out) each time, and his average dropped by 1. What was his final average?
6. On a river which runs at 3 km per hour a ferry travels upstream to a certain place and then returns, the total travelling time being 2 hours, and the total distance 22.5 km. Find what the speed of the ferry would be in still water.
7. O is the centre of a circle of radius 37 cm, and the length of a chord MB ia 24 cm. Find the area of triangle OMN.
8. Two equal chords intersect inside a circle. Prove that the line joining their point of intersectio to the centre of the circle bisects the angle between the chords.
9. After a certain number of matches a bowler has had 200 runs knocked off him. In the next match he takes 2 wickets for 42 runs, and increases his average (runs per wicket) by 1. How many wickets has he now taken?
10. If one tap can fill a bath in 6 minutes and another in 12, how long will they take when both are turned on together?
The answers to the above questions are forthcoming in a future post. Solving math problems is a hobby for me. I hope you will find these and others quite refreshing.
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