1. Two circles touch externally. The sum of their areas is 130π sq. cm and the distance between their centres is 14 cm. Find the radii of the CIRCLES?
2. Find the point on the x-axis which is equidistant from the points A(−2, 5) and B(2,−3)
3. Construct a regular hexagon of side 2.5 cm.
4. If x + y – z = 4 and x2 + y2 + z2 = 30, then find the value of xy – yz – zx.
5. Prove that the perimeter of a triangle is greater than the sum of its three medians.
6. If the mean of five observations x, x + 2, x + 4, x + 6, x + 8 is 13, find the value of x, and hence, find the mean of the last three observations.
7. If the mean of five observations x, x + 2, x + 4, x + 6, x + 8 is 13, find the value of x, and hence, find the mean of the last three observations.
8. A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litres of water can it hold? (Given 1 m3 = 1000 litres)
9. If P is the centre of the circle with radius 6.7 cm, d(P, Q) = 7.6 cm, d(P, R) = 5.7 cm, find the positions of points R and Q.
10. Solve the following simultaneous equations using the graphical method: x + y = 8; x – y = 2
11. The line segments joining the mid-points M and N of parallel sides AB and DC, respectively, of a trapezium ABCD is perpendicular to both sides AB and DC. Prove that AD = BC.
12. Each equal angle of an isosceles triangle is less than the third angle by 15 degrees. Find the angles
13. One pipe can fill a cistern in 3 hours less than the other. The two pipes together can fill the cistern in 6 hours 40 minutes. Find the time that each pipe will take to fill the cistern.
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