Question 319.
The figure shows a triangle ABC. The incircle O is tangent to AC at D. M is the midpoint of AC. Line AE is perpendicular to BO extended. Prove that the measure of DM is equal to half the measure of CE.
=> Δs ABL and EBL are congruent
=> BE = AB = c
=> CE = BC - BE = a - c ... (1)
DM
= AM - AD
= b/2 - rcot(A/2)
= b/2 - (s - a)
= b/2 - [(a+b+c)/2 - a]
= - a/2 - c/2 + a
= (a - c)/2 ... ... ... ... (2)
From (1) and (2),
DM = (1/2) CE.
Link to YA!
The figure shows a triangle ABC. The incircle O is tangent to AC at D. M is the midpoint of AC. Line AE is perpendicular to BO extended. Prove that the measure of DM is equal to half the measure of CE.
Answer 319.
In right Δs ABL and EBL,
side BL is common and
∠ABL = ∠EBL=> Δs ABL and EBL are congruent
=> BE = AB = c
=> CE = BC - BE = a - c ... (1)
DM
= AM - AD
= b/2 - rcot(A/2)
= b/2 - (s - a)
= b/2 - [(a+b+c)/2 - a]
= - a/2 - c/2 + a
= (a - c)/2 ... ... ... ... (2)
From (1) and (2),
DM = (1/2) CE.
Link to YA!
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