Does anyone know how to find the radius of an inscribed angle in a rhombus?

i need help with geometry.


If one side of a rhombus is 25 and the longer diagonal is 40, find the


a)length of the shorter diagonal


b)area of the rhombus


c)length of the altitude


d)radius of the inscribed circle





i got a,b,and c correct.


a)30


b)600


c)24





but i have no idea how to find the radius of the inscribed circle. PLEASE HELP!Does anyone know how to find the radius of an inscribed angle in a rhombus?
The radius of the inscribed circle is simply half the altitude. Inscribed means the biggest circle fits inside the rhombus.Does anyone know how to find the radius of an inscribed angle in a rhombus?
Hi Trist





I find that the DIAMETER of the inscribed circle is 24 and not the radius.





Let me give you the reasoning





The rhombus is symmetrical about the intersection of the two diagonals, so obviously the intersection of the two diagonals is the centre of the inscribing circle.YES?


ALSO


The inscribing circle will make the sides of the rhombus tangents to the circle.YES?


SO


the radius of the inscribing circle will be perpendicular to the side at the point of tangency. YES?


IN OTHER WORDS


The radius at the point of tangency is the HEIGHT of the triangle (one of the 4 congruent triangles of the rhombus). YES?





Now to the maths


Area of 1 triangle = Area of rhombus / 4 = 600/4 = 150


Area of 1 triangle is also = b*h/2 = 150


25*h/2 = 150


h = 150*2/25 = 12


AND


h = r


SO


r = 12





I hope that's understandable!!!





Shy