Question

In the given figure, AB is the chord of a circle with centre O. AB is produced to C such that BC$=$OB. CO is joined and produced to meet the circle in D. If $\angle$ACD$=y^0$ and $\angle$AOD$=x^0$ then $\angle x^0=?$

• A. $y^0$
• B. $2y^0$
• C. $3y^0$
• D. None of these

Answer 1

The correct option is C $3y^0$

Given $OB=BC$

$\therefore \measuredangle BOC=\measuredangle BCO=y°$

$\therefore \measuredangle OBC=180°-2y$

$\therefore \measuredangle ABO=2y°$

$AO=OB$ ( both are radius )

$\therefore \measuredangle OAB=\measuredangle ABO=2y°$

$\therefore \measuredangle AOB=180°-4y$

Now, $x+\measuredangle AOB+\measuredangle BOC=180°$

$\Rightarrow x+180-4y+y=180°$

$\Rightarrow x=3y°$

Hence, the answer is $3y°.$