If P is a point on the median AD of a ΔABC, then ar (ΔABP) = ar(ΔACP).

In ∆ABC,

Since, AD is the median


Thus, BD = DC


Let the height of ∆ABC be h


ar(∆ABD) = ar(∆ABD)


1/2 × h × BD = 1/2 × h × BD


1/2 × h × BD = 1/2 × h × CD


ar (∆ABD) = ar (∆ADC)


Let H be the height of ∆BPD and ∆PDC


ar (∆BPD) = ar (∆PDC)


Now, ar(∆ABD) = ar (∆ABP) + ar (∆BPD)


And, ar(∆ACD) = ar(∆ACP) + ar(∆PDC)


Thus, ar(∆ABP) = ar(∆ACP)


Option A is correct

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