Question:
In the given figure, if AP = PB, then
(a) AC = AB
(b) AC = BC
(c) AQ = QC
(d) AB = BC
Solution:
The given figure is below
It is given that,
AP = PB
We know that
PB = BR(tangents from an external point are equal)
From the above two equations, we can say that,
AP = BR …… (1)
Also,
AP = AQ(tangents from an external point are equal) …… (2)
From equations (1) and (2), we have,
AQ = BR …… (3)
Also,
QC = CR(tangents from an external point are equal) …… (4)
Adding equations (3) and (4), we get,
AQ + QC = BR + CR
By looking at the figure we can write the above equation as,
AC = BC
The correct answer is option (b).