Let ABCD be a quadrilateral and let P be the intersection point of the diagonals AC and BD. Let angleADB = 2angleACB, AD = BD = 3, and BP = 1. What is the product of the length of the segments AP and CP?
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Answer:
Draw a line EO such that
EO || AB
EA
DE
=
BO
DO
….(i) [ Proportionality Theorem]
Also,
BO
AO
=
DO
CO
Given
BO
DO
=
AO
CO
...(ii)
From equation (i) and (ii), we get
EA
DE
=
AO
CO
By using converse of Basic Proportionality Theorem, EO || DC also EO || AB
AB || DC.
Hence, quadrilateral ABCD may be a trapezium with AB || CD or may be a parallelogram.
So correct option can be both A and B
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