Final answer:
To find the value of AR in the figure, we need to use the fact that RE is parallel to BC. We can conclude that triangles RAE and BCD are similar triangles, and we can use the ratios of their corresponding sides to solve for AR.
Step-by-step explanation:
To find the value of AR in the figure, we need to use the given information that RE is parallel to BC.
Since RE is parallel to BC, we can conclude that angles RED and BCD are equal. We also know that angles RED and RAE are corresponding angles formed by transversal intersecting parallel lines. Therefore, angles RAE and BCD are also equal.
Since angles RAE and BCD are equal, we can conclude that triangles RAE and BCD are similar triangles. This means that the ratios of their corresponding sides are equal:
- AE/CD = AR/BC
We can substitute the length of CD which is known as 'r' and the length of BC which is known as 'c' into the equation:
- AE/r = AR/c
Finally, we can solve for AR by multiplying both sides of the equation by 'c' and then dividing by 'r':
- AR = (AE/r) * c
So, the value of AR in the figure is (AE/r) * c.