Question
Download Solution PDFIn triangle ABC, the bisector of angle BAC cuts the line BC at D. If BD = 6 and BC = 14 then what is the value of AB ∶ AC?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
In triangle ABC, the bisector of angle BAC cuts the line BC at D.
BD = 6 and BC = 14
Concept used:
Angle Bisector Theorem: The angle bisector of a triangle divides the opposite side into two parts proportional to the other two sides of the triangle.
Calculation:
DC = BC - BD = 14 - 6 = 8 cm
According to the Angle Bisector Theorem,
BD/CD = AB/AC
⇒ 6/8 = AB/AC
⇒ AB : AC = 3 : 4
∴ The value of AB : AC is 3 : 4.
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