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In a triangle ABC, the internal bisector of the angle A meets BC at D. If AB = 4, AC = 3 and ∠ A = 600, then length of AD is :
- a)2√3
- b)(12√3) / 7
- c)(15√3) / 8
- d)(6√3) / 7
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
In a triangle ABC, the internal bisector of the angle A meets BC at D....
Let BC = x and Ad = y, then as per bisector theorem,
BD /DC = AB /AC = 4 /3
Hence, BD = 4x/7 and DC = 3x/7
Now, in Δ ABD using cosine rule,
cos 300 = [{42 +y2 - (16x2/49)} /2*3*y]
Or, 4√3y =[{16 +y2 - (16x2/49)}] --------- (i)
Similarly in Δ ADC,
cos 300 = [{32 +y2 - (9x2/49)} /2*3*y]
Or, 3√3y =[{9 +y2 - (9x2/49)}] --------- (ii)
From equation (i) and (ii), we get
y = 12√3 /7.
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In a triangle ABC, the internal bisector of the angle A meets BC at D....
BD = 2, then find CD.
We can use the angle bisector theorem to find CD. The theorem states that the internal bisector of an angle in a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.
Let CD = x. Then, by the angle bisector theorem,
AB/BD = AC/CD
Substituting the given values, we get:
4/2 = 3/x
Simplifying, we get:
2 = 3/x
Multiplying both sides by x, we get:
2x = 3
Dividing both sides by 2, we get:
x = 3/2
Therefore, CD = 3/2.
We can use the angle bisector theorem to find CD. The theorem states that the internal bisector of an angle in a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.
Let CD = x. Then, by the angle bisector theorem,
AB/BD = AC/CD
Substituting the given values, we get:
4/2 = 3/x
Simplifying, we get:
2 = 3/x
Multiplying both sides by x, we get:
2x = 3
Dividing both sides by 2, we get:
x = 3/2
Therefore, CD = 3/2.
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In a triangle ABC, the internal bisector of the angle A meets BC at D. If AB = 4, AC = 3 and∠A = 600, then length of AD is :a)2√3b)(12√3) / 7c)(15√3) / 8d)(6√3) / 7e)None of theseCorrect answer is option 'B'. Can you explain this answer?
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