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Geometry Level 4

In a △ A B C , A B = A C . \triangle ABC, AB=AC. A transversal intersects AB and AC internally at K K and L L respectively. It intersects B C BC produced at M . M. If K L = 2 L M KL=2LM , fiind K B L C \dfrac{KB}{LC} .


The answer is 3.

Ayush G Rai by Ayush G Rai , 20, India

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2 solutions

Ayush G Rai
May 27, 2016

Draw K D ∥ L C , KD\parallel LC, meeting B C BC at D . D. Then
∠ K D B = ∠ L C B = ∠ K B D ⇒ K B = K D . \angle KDB=\angle LCB=\angle KBD\Rightarrow KB=KD.
Therefore K B L C = K D L C = K M L M = 3 . \frac{KB}{LC}=\frac{KD}{LC}=\frac{KM}{LM}=\boxed 3.

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Ahmad Saad
May 31, 2016

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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