ABC is a right-angled triangle, right-angled at A in such a way that AB = AC and the bisector of angle B intersects the side AC at D. DM is perpendicular to BC, intersecting BC at M. If AB = 12 cm and BC = cm, then find the length of side AD.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. cm.
In the given right-angled triangle,
AB = AC, AD is the angle bisector of ∠BAC
Using the property of right-angled triangle and angle bisector theorem;
According to the question;
⇒ AD/DC = AB/BC
Let AD be x, DC = 12 - x, AB = AC = 12
⇒ x/(12 - x) = 12/
⇒ √2x = 12 - x
⇒ x(√2 + 1) = 12
⇒ x = 12/(√2 + 1)
⇒ x = 12(√2 - 1)