Mathematics
In △ABC, ∠B = 35°, ∠C = 65° and the bisector AD of ∠BAC meets BC at D. Arrange the sides AD, BD and CD in ascending order of their lengths.
Triangles
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Answer
In △ADB,
⇒ ∠BAD + ∠ADB + ∠ABD = 180°
⇒ 40° + ∠ADB + 35° = 180°
⇒ ∠ADB + 75° = 180°
⇒ ∠ADB = 180° - 75°
⇒ ∠ADB = 105°.
We know that,
The shortest side of a triangle has the smallest angle opposite to it.
In triangle ABD,
Since,
⇒ ∠B < ∠A
⇒ AD < BD …….(1)
From figure,
∠ADB + ∠ADC = 180° (Linear pair)
⇒ ∠ADC + 105° = 180°
⇒ ∠ADC = 180° - 105°
⇒ ∠ADC = 75°
In triangle ACD,
Since,
⇒ ∠A < ∠C
⇒ CD < AD ……..(2)
From eq.(1) and (2) we have:
⇒ CD < AD < BD
Hence, CD < AD < BD.
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