In ΔABC, ∠B = 90°, AB = 8 cm and BC = 15 cm. D is a point on BC such…

As , AD is bisector of angle ∠A.

So, \(\frac{BD}{DC}\) = \(\frac{AB}{AC}\)

By using pythagoras theorem ,

( Hypotenuse )² = ( Perpendicular )² + ( Base )²

( AC )² = ( AB )² + ( BC )²

( AC )² = ( 8 )² + ( 15 )²

( AC )² = 64 + 225 = 289

AC = 17

Using , \(\frac{BD}{DC}\) = \(\frac{AB}{AC}\)

\(\frac{BD}{DC}\) = \(\frac{8}{17}\)

So, BD and DC id divided in ratio 8 : 17

According to question,

8R + 17R = 15

25R = 15

1R = \(\frac{3}{5}\)

Now, BD = 8R = 8 x \(\frac{3}{5}\)

= 4.8 cm