4. In triangle \( A B C \), points \( D \) and \( E \) lie on \( A B \) and \( A C \), respectively, such that \( A D=D E=E B=B C \) and \( \angle A B \bar{C}=144^{\circ} \). Determine \( \angle A \). In driehoek \( A B C \) lê punte \( D \) en \( E \) op onderskeidelik \( A B \) en \( A C \), sodat \( A D=D E=E B=B C \) en \( \angle A B C=144^{\circ} \). Bepaal \( \angle A \).

Analitik düzlemde \( d_{1}: 2 x+y-12=0 \) ve \( d_{2}: x-y+6=0 \) doğruları veriliyor. 9. \( d_{1} \) ve \( d_{2} \) doğruları ile \( x \) ekseni arasında kalan alanın kaç birimkare olduğunu bulu- nuz. 10. \( d_{1} \) ve \( d_{2} \) doğruları ile eksenler arasında kalan alanın kaç birimkare olduğunu bulunuz.

В \( \triangle \mathrm{ABC} \angle \mathrm{C}=90^{\circ} \). Точка Д ве лежит в плоскости ABC , причем ДС \( \perp \mathrm{AC} \). Дожажите, что прямая AC перпевдикудярна к плоскости ДСВ. Постройте сечение тетразра гиоскостьо, проходящей через точки \( \mathrm{K}, \mathrm{M} \) и P .

Point \( C \) with coordinates \( (50,30) \) is mapped onto \( C^{\prime} \) through a translation by vector \( \langle-3,6\rangle \). What are the coordinates of \( C^{\prime} \) ? - \( (47,36) \) - \( (53,24) \) - \( (47,24) \) - \( (53,36) \)

1. \( A(4 ; 3 ;-2), \quad B(-3 ;-1 ; 4), C(2 ; 2 ; 1\} ; \) \( a=\overrightarrow{A B}, b=\overrightarrow{A C}, c=\overrightarrow{C B}, \quad d=2 c-5 b, \quad l=C B, \quad \alpha=4, \quad \beta=3 \) 2. \( a=5 m-3 n, \quad b=m+3 n, \quad|m|=1, \quad|n|=1, \quad \varphi=\frac{\pi}{2} \). 3. \( a=\{1 ; 3 ; 0\}, \quad b=\{2 ;-1 ; 1\}, \quad c=\{0 ;-1 ; 2\}, \quad d=\{6 ; 12 ;-1\} \).

1. In a circle with centre \( O \) and radius \( 5 \mathrm{~cm}, A B \) is a chord of length 8 cm . If \( O M \perp A B \), what 2. In a length of \( O M \) ? in the length of centre \( O \) and radius \( 13 \mathrm{~cm}, A B \) is a chord. If \( O M \perp A B \) and \( O M=5 \mathrm{~cm} \), wh 3. In a circle of radius 7 cm , find the distance of a chord of length 9 cm from the centre. 4. In a circle of radius 13 cm , a chord is drawn at a distance 12 cm from the centre. Find th length of the chord. 5. A chord of a circle is 6 cm in length and its distance from the centre is 4 cm . Find the radius of the same circle.