(C) is a circle of center O. diameter [AB].
• OA= OB = 3 cm.
P is the point of [AB) such that OP = 5 cm
. E is a point of (C) such that PE = 4 cm.
• (D) is the tangent to (C) at A.
• (PE) cuts (D) in J.
♦ 1) Reproduce this figure. It will be used and completed by the remaining parts of this problem.
2) Prove that (PE) is tangent to (C) at E. Deduce that JA = JE.
3) Let JE = JA = x, where X is a measure of length in cm. a) Applying Pythagoras' theorem in triangle APJ, show that x=6 b) Deduce that triangie ABJ is a right isosceles triangle. (C) 4) (JB) cuts (C) in a second point F. Prove that F is the midpoint of [JB] and that (FO) is the perpendicular bisector of [AB]
5) Let L be a point on [EJ], such that EL = 2.4 cm. Show that (OE) // (AL). ​