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Geometry Level 4

A right angled triangle ABC was given in which angle C is 90 degrees and \( BC = 4 \). \(D\) is a point on \(BC \) such that \( AD = 3 \). Given that the perimeter of triangle ABD is equal to the perimeter of triangle ADC. Find:-

\[ BD:DC.\]

This ratio can be expressed as a:b where a and b are co-prime numbers. What is \( a + b \)?

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