In ∠ABC, ∠C = 90o, AC = 5 cm and BC = 12 cm. The bisector of ∠A meets BC at D. What is the length of AD?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e (5√(13))/(3) cm
The triangle ABC is the right-angled triangle, the Pythagoras theorem applies to it which is as
⇒ AC2 + BC2 = AB2
⇒ (5)2 + (12)2
⇒ AB = 13 cm
By the angle bisector theorem
⇒ AB/BD = AC/CD
⇒ 13/BD = 5/CD
Let BD equals 'x'
⇒ 13/x = 5/(12 - x)
⇒ x = 26/3 cm
⇒ CD = 12 - 26/3 = 10/3 cm
So,
AD2 = AC2 + CD2
⇒ AD = (5√(13))/(3) cm