Answer:
EC = 12.12
Step-by-step explanation:
Given H and B are circles of radius 7
ED = 7
CB = 7, so DB is also 7
Therefore, EB = ED + DB
= 7 + 7
= 14
Since IC is tangent at C we know that it is making a right angle to the radius CB.
Therefore, Triangle EBC is a right angle triangle where CB = 7 and EB = 14
Therefore from Pythagoras theorem,
[tex](EB)^{2}= (EC)^{2}+(CB)^{2}[/tex]
[tex](EC)^{2}= (EB)^{2}-(CB)^{2}[/tex]
[tex](EC)^{2}= (14)^{2}-(7)^{2}[/tex]
[tex](EC)^{2}= 196-49[/tex]
[tex](EC)^{2}= 147[/tex]
Therefore, EC = 12.12
