We have, One trapezium ABCD. AB∥CD and AD⟂AB And, the trapezium has an incircle which touches AB at E and CD at F. Here EB=25cm and FC=16cm If we draw one line from E to F which is pass through centre of circle then EF is tangent to circle and it makes 90∘ angle with AB and CD respectively. Then EF∥AD We draw a line from C to EB at position N means CN⟂AB
By the rule of tangent if two tangents which touches at different position in a circle has meet at one point then length is same from the particular position to tangent. So, here MB and EB is tangent to circle and meet at B. BM=EB=25cm And, FC and MC is tangent to circle and meet at C. FC=MC=16cm Then CB=16+25=41cm In a ∆CNB, 412=92+CN2 ⇒CN=40cm We can see CN=FE=AD=40cm So. diameter is 40cm.