The digits of a 3 digit number \(A\) were written in reverse order and this is the number \(B\). Is it possible to find a value of \(A\) such that the sum of \(A\) and \(B\) has only odd numbers as its digits?
Let \(x\) be a 2 digit number. Let \(A\), \(B\) be the first (tens) and second (units) digits of \(x\), respectively. Suppose \(A\) is twice as large as \(B\). If we add the square of \(A\) to \(x\) then we get the square of a certain whole number. Find the value of \(x\).
Construct a triangle with the side \(c\), median to side \(a\), \(m_a\), and median to side \(b\), \(m_b\).
Construct a triangle with the side \(a\), the side \(b\) and height to side \(a\), \(h_a\).
Inside an angle two points, \(A\) and \(B\), are given. Construct a circle which passes through these points and cuts the sides of the angle into equal segments.
Two segments \(AB\) and \(A'B'\) are given on a plane. Construct the point \(O\) so that the triangles \(AOB\) and \(A'OB'\) are similar (the same letters denote the corresponding vertices of similar triangles).
Using a right angle, draw a straight line through the point \(A\) parallel to the given line \(l\).
Prove that \(S_{ABC} \leq AB \times BC/2\).
Prove that \(S_{ABCD} \leq (AB \times BC + AD \times DC)/2\).
Prove that \(\angle ABC > 90^{\circ}\) if and only if the point \(B\) lies inside a circle with diameter \(AC\).