Question

in given equilateral triangle ABC , AB = 10cm and CD is angular bisector of

Answer 1

⇰ Question

• In given quadrilateral triangle ABC, AB is 10 cm and CD is angular bisector of ∠ACD. Then the length of CD is ?

⇰ Given

• ΔABC is a equilateral triangle
• AB = 10 cm
• CD is angular bisector of ∠ACD

⇰ To find

• CD

⇰ Solution

• In ΔADC, ∠ADC = 90°
• CD² = AC² - AD²  (Pythagoras Theorem)

➝ AD length is 5 cm as in the question they gave CD is a angular bisector of ∠ACD, which means CD divides ΔABC to ΔADC and ΔDCB, we know AB is 10 cm , therefore length of AD and AB will be 5 cm

• CD² = 10² - 5²
• CD² = 100 - 25
• CD² = 75
• CD = √75
• CD = √25×3
• CD = ⁵√3

⇰ Length of CD = ⁵√3 cm