Circles H and I have the same radius. JK, a perpendicular bisector to HI, goes through L and is twice the length of HI. If HI acts as a bisector to JK, what type of triangle would HKI be?a) right triangleb) special right trianglec) equilateral triangled) isosceles triangle

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par5o4nr4z · Accepted Answer

Step 1The given data is:Circles H and I have the same radiusJK, a perpendicular bisector to HI, goes through L and is twice the length of HI. If HI acts as a bisector to JKTo describe triangle HKI.Step 2Now draw the given data:Let the length of HI be 2x, therefore the length of JK is 4xJK is the bisector of HI, thereforeHL=LI=x HI is the bisector of KJ, then JL=LK=xStep 3In triangle △HKIThe length of side HI is 2xIn △HLK, apply Pythagorean theorem:HK2=HL2+KL2HK2=x2+(2x)2HK2=x2+4x2HK2=5x2HK=5x2HK=5xSimilarly, in △ILK, apply Pythagorean theorem:IK2=IL2+KL2IK2=x2+(2x)2IK2=x2+4x2IK2=5x2IK=5x2IK=5xStep 4In triangle △HKIThe length of side HI is 2xThe length of side HK is 5xThe length of side IK is 5xTherefore, HK=KIThus, the given triangle HKI is an isosceles triangle.Hence, option (D) is correct.

Circles H and I have the same radius. JK, a

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