Final answer:
The triangle HKI is an isosceles triangle.
Step-by-step explanation:
The given information states that circles H and I have the same radius. JK is a perpendicular bisector to HI and is twice the length of HL. HL is also a bisector to JK. Based on this information, we can determine the type of triangle HKI.
Since HL acts as a bisector to JK, it divides JK into two equal parts, making HK and KI equal. Therefore, triangle HKI is an Isosceles triangle.