In △ABC, M is the midpoint of the sides AB. N is a point of △ABC such that CN is the bisector of ∠C and CN Ʇ NB. What is the length (in cm) of MN, if BC = 10 cm and AC = 15 cm?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 2.5
In the given figure,
∠BNC = ∠ONC = 90°
∠OCN = ∠BCN
CN = NC ( common)
△BNC is congruent to △ONC.
So, OC = OB = 10 cm and BN = ON
AC = 15
OA = 15 - 10 = 5 cm.
Now in △ABO,
M and N are the midpoints of AB and OB.
MN = OA/2 = 5/2 = 2.5