5.3. A diameter and a chord, which is equal to the radius, are passed from the given point of the circle. Find the angle between them.

23. Find the equation of a line. Whoso intercepts on \( x \) and \( y \) axis are 4 and -6

6. ABCD is a quadrilateral, and AC and BD are its diagonals. Is \( \mathrm{AB}+\mathrm{BC}+\mathrm{CD}+\mathrm{DA}>\mathrm{AC}+\mathrm{BD} \) ? 7. ABCD is a quadrilateral and \( O \) is any point in its interior in the given figure Show that \( A B+B C+C D+D A<2(O A+O B+O C+O D) \).

Find equation of straight line through \( (-1,4) \) and perpendicular to the line passing through \( (3,0) \) and \( (1,-2) \).

In a right triangle, the lengths of the legs are given as 12 units and 5 units. Use the Pythagorean theorem to find the length of the hypotenuse.

9. ABC is a triangle in which \( \mathrm{m} \overline{\mathrm{BC}}=\mathrm{m} \overline{\mathrm{CA}}=2 \mathrm{~m} \overline{\mathrm{AB}} \). Internal bisector of \( \angle \mathrm{A} \) meets \( \overline{\mathrm{BC}} \) at D and \( \overline{\mathrm{DE}} \) is drawn parallel to \( \overline{\mathrm{CA}} \) meeting \( \overline{\mathrm{AB}} \) at E . Find \( \mathrm{m} \overline{\mathrm{DE}}: \mathrm{m} \overline{\mathrm{AB}} \).