Question

Find the value of $x$ and $y$ from the figure.

• A. $x=7,y=3$
• B. $x=5,y=6$
• C. $x=8,y=4$
• D. $x=11,y=9$

Answer 1

The correct option is A $x=7,y=3$

Perpendicular from centre to the chord bisects the chord

Therefore, $2y+1=y+4$

$\Rightarrow 2y-y=4-1$

$\Rightarrow y=3$

Perpendicular from centre to the chord bisrects the arc subtended by the chord

Therefore, ${(5x-18)}^{\circ }={(3x-4)}^{\circ }$

$\Rightarrow 5x-3x=-4^{\circ }+{18}^{\circ }\Rightarrow 2x={14}^{\circ }\Rightarrow x=\frac{{14}^{\circ }}{2}=7^{\circ }$

Option A is correct.