Give an example of each of two irrational number whose sum is a rational number.

In the figure, AP and DP are bisectors of ∠D. Prove that 2∠APD = ∠B + ∠C.

At his usual running rate, Rahul can travel 12 miles downstream in a certain river in 6 hours lessthan it takes him to travel the same distance upstream. But if he could double his usual rowingrate for his 24 miles round trip the downstream 12 miles would then take only one hour less thanthe upstream 12 miles. What is the speed of the current in miles per hour?

A train covered a certain distance at a uniform speed. If the train would have been 10km/hr faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10km/hr, it would have taken 3 hours more than the scheduled time. The distance covered by the train is A. 300kmB. 400kmC. 600kmD. 260km

Prove that the quadrilateral formed (if possible) by the internal angle bisectors of any quadrilateral is cyclic.