SOLUTION: In the diagram below, EFGH is a rhombus formed by connecting the mid-points of the sides of the rectangle ABCD. The rectangle is circumscribed by the circle with center O. Find the

Question 1148559: In the diagram below, EFGH is a rhombus formed by connecting the mid-points of the sides of the rectangle ABCD. The rectangle is circumscribed by the circle with center O. Find the area, in cm2 of the rhombus if OF=15cm, and JH=6cm.
Diagram: https://ibb.co/rwnM6f9
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

FK = JH = 6, so the radius of the circle is OF+FK = OF+JH = 21.

OC is also a radius of the circle, so OC = 21.

Then triangle OFC is a right triangle and we know OF=15 and OC=21; the Pythagorean Theorem then tells us

Then the diagonals of the rhombus are 30 and 12*sqrt(6).

The area of a rhombus is half the product of the diagonals:

RELATED QUESTIONS
In the diagram, EFGH is a rhombus formed by connecting the mid-points of the sides of the (answered by ikleyn)

In the diagram below, EFGH is a rhombus formed by connecting the midpoints of the sides... (answered by ikleyn)

Prove that the quadrilateral formed by connecting the midpoints of the sides of... (answered by ikleyn,Edwin McCravy)

Question: Take a Rectangle ABCD. Find out the mid points of all sides denotes it... (answered by orca)

The diagonals of a parallelogram ABCD are each subdivided into 6 equal parts, then... (answered by ikleyn)

show that the quadrilateral formed by joining the mid-points of the sides of a square is... (answered by MathLover1)

Gold Medal Problem ABCD is a square. POints EFGH are teh midpoints of the sides. AB =1 (answered by Edwin McCravy)

In the diagram of rhombus ABCD, the lengths of the sides AB and BC are represented by 3x... (answered by robertb)

Diagonal AC of a rhombus ABCD is equal to one of its sides BC. Find the angles of the... (answered by solver91311)