MCQ
In the given figure, if $AP = PB,$ then $AC =$
- ✓$AC = BC$
- B$AB = BC$
- C$AQ = QC$
- D$AC = AB$
✓
Answer
Correct option: A.
$AC = BC$
Since Tangents from an external point to a circle are equal
$\therefore PB = BR …(i)$
$PA = AQ …(ii)$
$CQ = CR ...(iii)$
Adding eq. $(i)$ and $(iii),$ we get
$PB + CQ = BR + CR$
$\Rightarrow AP + CQ = BC \ [$Given : $PB = AP]$
$\Rightarrow AQ + CQ = BC\ [$From eq. $(ii) \ AP = AQ]$
$\Rightarrow AC = BC$
$\therefore PB = BR …(i)$
$PA = AQ …(ii)$
$CQ = CR ...(iii)$
Adding eq. $(i)$ and $(iii),$ we get
$PB + CQ = BR + CR$
$\Rightarrow AP + CQ = BC \ [$Given : $PB = AP]$
$\Rightarrow AQ + CQ = BC\ [$From eq. $(ii) \ AP = AQ]$
$\Rightarrow AC = BC$
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