幾何與角

In the figure, $ABC$ is a semicircle with $\widehat{BC}=7$ and $\angle ACB=55^\circ$. Find $\widehat{AB}$.

Which of the following statements about the triangles in the figure must be true?

In the figure, $ABD$ and $ACE$ are straight lines. If $AC:CE=3:4$, then $BC:DE=$

The figure shows a circle with diameter $AD$. If $AB=BC=CD$, find $x+y+z$.

In the figure, $XAB$ and $XDC$ are straight lines. If $DX=5$, $AX=6$ and $AB=4$, find $CD$.

In the figure, $BE$ and $BF$ are tangents to the circle at $A$ and $C$ respectively. If $\angle ADC=100^\circ$, then $\angle ABC=$

In the figure, $ABCD$ is a parallelogram and $ADH$, $EBC$ and $EFGH$ are straight lines. If $AD=6$, $DH=4$ and $EB:BC=3:4$, then $EF:GH=$

In the figure, $ABC$ and $AFED$ are straight lines. $\angle ABF=\angle CDE$ and $BE/\!/CD$. Which of the following triangles are similar? I. $\triangle ABF$ II. $\triangle AEB$ III. $\triangle ADC$

In the figure, $ABCDEFGH$ is a regular octagon. $x+y+z=$

In the figure, $O$ is the centre of the semicircle $ABCD$ and $BC/\!/AD$. If $\angle COD=42^\circ$, then $x=$