ABC is a right angle triangle . right angle at B. the external bisector of angleA meets angleB produced at D. If AC =25cm, BC=7cm. find the value of CD?

Question

Answer

Given data:
- ABC is a right angle triangle with right angle at B.
- The external bisector of angle A meets angle B produced at D.
- AC = 25 cm
- BC = 7 cm

Objective:
To find the value of CD.

Solution:

Step 1: Finding the length of AB
Given that ABC is a right angle triangle, we can use the Pythagorean theorem to find the length of AB.
Using Pythagorean theorem, we have:
AB^2 + BC^2 = AC^2
AB^2 + 7^2 = 25^2
AB^2 + 49 = 625
AB^2 = 576
AB = √576
AB = 24 cm

Step 2: Finding the length of BD
Since AD is the external bisector of angle A, we can apply the angle bisector theorem to find the length of BD.
AB/BC = AD/DC
24/7 = AD/DC
AD = (24/7) * DC

Step 3: Finding the length of CD
Since D is the point where the external bisector of angle A meets angle B produced, we have:
AD + DC = AC
(24/7) * DC + DC = 25
(24 + 7) * DC = 25 * 7
31 * DC = 175
DC = 175/31
DC = 5.645 cm (approx.)

Therefore, the value of CD is approximately 5.645 cm.

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