Question

In a AABC, ZB=90®, AB=1cm, BC = 2 cm and M is the mid-point of BC. D is a point on CA such that MD1 CA. What is the
length of the line segment MD?​

Answer 1

Answer:

R.E.F. Image.

In △ABC,

(1) M is the mid point of AB and

MD∥BC

D is the mid point of AC

(2) As MD∥BC &

AC is transversal

∠MDC+∠BCD=180

∘

∠MDC+90

∘

=180

∘

⇒∠MDC=90

∘

⇒MD⊥AC

(3) In △AMD and △CMD

AD=CD

∠ADM=∠CDM

DM=DM

△AMD≅△CMD

AM=CM⇒AM=

2

1

AB⇒CM=AM=

2

1

AB