AB=36cm and M ismid point ofAB semicircles are drawn inAB,AMandMBas diameter.a circlewith centreO touches all three semi
circle find radius?
To find the radius of the circle with center O that touches all three semicircles, we can use the concept of tangents.
Let's first draw the diagram:
A M B
**********************
****** ******
**** ****
** **
O O
In the given scenario, AB = 36 cm and M is the midpoint of AB.
Now, let's use the concept that a tangent to a circle is perpendicular to the radius drawn to the point of tangency.
1. Since M is the midpoint of AB, we can infer that the length of AM = MB = 18 cm.
2. The circle with center O touches the semicircle with diameter AB at point M. Since AM and BM are radii of the semicircle, OM will also be a radius of the circle with center O.
3. The length of OM can be found by using the Pythagorean theorem. The length of OM = sqrt(AM^2 - OA^2), where OA is the radius of the semicircle.
4. The length of AM is 18 cm. To find OA, we need to calculate the radius of the semicircle. The radius of a semicircle is half the length of the diameter. Since the diameter AB is given as 36 cm, the radius of the semicircle is 36/2 = 18 cm.
5. Now we substitute the values into the equation: OM = sqrt(18^2 - 18^2) = sqrt(324 - 324) = sqrt(0) = 0
Therefore, the radius of the circle with center O is 0 cm.