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A right ∆ABC with ∠B=90° has incircle(O). D is tangent point on AC. DO extends meet BC at E. If DE=9 and AD=8, find AB.

An obtuse angled triangle has integral sides and one acute angle is twice the other. Find the smallest possible perimeter

Seven children A, B, C, D, E, F and G started walking from the same point at the same time, with speeds in the ratio of 1 : 2 : 3 : 4 ...

How many distinct solutions (not necessarily real) exist for the equation \[ (x-1)\big(x^2-1\big)\big(x^3-1\big)\cdots \big(x^{10}-1\big)=0\,? \]

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