Question

\( 2^{\circ} \) Show that \( A M N=A C B \) and that : \[ \widehat{A C B}+\widehat{N M B}=180^{\circ} \text {. } \] 10 Consider \( (C) \) a circle of center \( O \) and of radius \( R \). \( [O A] \) and \( [O B] \) are two perpendicular radii of \( (C) \). Consider \( C \) a point of the major arc \( \overparen{A B} \). The tangents at \( A \) and \( C \) to this circle intersect at \( M \). The line \( (C M) \) cuts the line \( (O B) \) at \( P \). Let \( D \) be the orthogonal projection of \( M \) on \( (O B) \). \( 1^{\circ} \) Show that the triangle \( P M O \) is isosceles of main vertex \( P \).

          \( 2^{\circ} \) Show that \( A M N=A C B \) and that :
\[
\widehat{A C B}+\widehat{N M B}=180^{\circ} \text {. }
\]
10 Consider \( (C) \) a circle of center \( O \) and of radius \( R \).
\( [O A] \) and \( [O B] \) are two perpendicular radii of \( (C) \).

Consider \( C \) a point of the major arc \( \overparen{A B} \). The tangents at \( A \) and \( C \) to this circle intersect at \( M \). The line \( (C M) \) cuts the line \( (O B) \) at \( P \). Let \( D \) be the orthogonal projection of \( M \) on \( (O B) \).
\( 1^{\circ} \) Show that the triangle \( P M O \) is isosceles of main vertex \( P \).

2^∘ Show that A M N=A C B and that :

A C B+N M B=180^∘.

10 Consider (C) a circle of center O and of radius R.
[O A] and [O B] are two perpendicular radii of (C).

Consider C a point of the major arc A B. The tangents at A and C to this circle intersect at M. The line (C M) cuts the line (O B) at P. Let D be the orthogonal projection of M on (O B).
1^∘ Show that the triangle P M O is isosceles of main vertex P.

Added by Hector S.

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