Question

ABC is a triangle right angled at C.A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D.AB=10 cm.Find (i) angle ADM (ii) length of CM. ​

Answer 1

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Answer 2

Step-by-step explanation:

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