SSC Government Jobs Exams Numerical Ability Geometry

the bisector of angle BAC of triangle ABC cuts BC at D and the circumcircle of the triangle at E, if DE=3cm ,AC=4 cm and AD=5 cm,then the length of AB is?

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SSC Other Question

Out of 30 teachers of a school,a teacher of age 60 years retired. In his place another teacher of age 30 years was appointed. As a result,the mean age of the teachers will
a)remain same
b)decrease by 2 years
c)decrease by 6 months
d)decrease by 1 year
The average age of 20 students in a class is 12 years. If the age of the teachers is also added then the average becomes 13 years. Find out the age of the teacher?