Here is some VBA code. make a tool button in ArcMap and put this behind the mouse down event. This should give you a radius that is equal in distance. this is done by centering the coordinate system origin on the point.
Private Sub Create_Circle_MouseDown(ByVal button As Long, ByVal shift As Long, ByVal x As Long, ByVal y As Long)
On Error GoTo EH
Dim pMxDoc As IMxDocument
Set pMxDoc = ThisDocument
Dim pMap As IMap
Set pMap = pMxDoc.FocusMap
Dim pAV As IActiveView
Set pAV = pMxDoc.ActivatedView
Dim pWGS84CoordSys As IGeographicCoordinateSystem
Dim pSpatialRefFactory As ISpatialReferenceFactory
Set pSpatialRefFactory = New SpatialReferenceEnvironment
Set pWGS84CoordSys = pSpatialRefFactory.CreateGeographicCoordinateSystem(esriSRGeoCSType.esriSRGeoCS_WGS1984)
Dim pCenterPoint As IPoint
Set pCenterPoint = pAV.ScreenDisplay.DisplayTransformation.ToMapPoint(x, y)
Dim pPCS As IProjectedCoordinateSystem
Set pPCS = ProjectToWGSAzimuthal(pCenterPoint.x, pCenterPoint.y)
Set pCenterPoint.SpatialReference = pMap.SpatialReference
pCenterPoint.Project pPCS
Dim pConstructCircleArc As IConstructCircularArc
Set pConstructCircleArc = New CircularArc
Dim inputRadius As String
inputRadius = InputBox("Enter Radius")
If inputRadius = "" Then Exit Sub
If Not IsNumeric(inputRadius) Then Exit Sub
If CDbl(inputRadius) <= 0 Then Exit Sub
Dim outRadius As Double
outRadius = ConvertUnits(CDbl(inputRadius))
pConstructCircleArc.ConstructCircle pCenterPoint, CDbl(outRadius), True
Dim pSegmentCollection As ISegmentCollection
Dim pPolygon As IPolygon
Dim pGraphContainer As IGraphicsContainer
Set pGraphContainer = pMxDoc.ActiveView
Dim pGCSelect As IGraphicsContainerSelect
Set pGCSelect = pMxDoc.FocusMap
Dim pElement As IElement
Set pElement = New PolygonElement
Set pSegmentCollection = New Polygon
pSegmentCollection.AddSegment pConstructCircleArc
Set pElement = New CircleElement
pElement.Geometry = pSegmentCollection
Dim pPoly As IPolygon
Set pPoly = pElement.Geometry
pPoly.Densify 0, 0
Set pPoly.SpatialReference = pPCS
pPoly.Project pWGS84CoordSys
pElement.Geometry = pPoly
Dim pLineSymbol As ISimpleLineSymbol
Dim pColor As IColor
Dim pLineColor As IRgbColor
Set pLineColor = New RgbColor
pLineColor.Red = 20
pLineColor.Green = 36
pLineColor.Blue = 255
Set pLineSymbol = New SimpleLineSymbol
pLineSymbol.Width = 2
pLineSymbol.Color = pLineColor
Set pColor = New RgbColor
pColor.NullColor = True
Dim pFillShpElem As IFillShapeElement
Dim pSFSymbol As ISimpleFillSymbol
Set pFillShpElem = pElement
Set pSFSymbol = New SimpleFillSymbol
pSFSymbol.Style = esriSFSHollow
pSFSymbol.Color = pColor
pSFSymbol.Outline = pLineSymbol
pFillShpElem.Symbol = pSFSymbol
Set pGraphContainer = pAV
pGraphContainer.AddElement pFillShpElem, 0
pGCSelect.SelectElement pFillShpElem
pMxDoc.ActiveView.PartialRefresh esriViewGraphics, Nothing, Nothing
Set pSpatialRefFactory = Nothing
Set pWGS84CoordSys = Nothing
Set pMxDoc = Nothing
Set pMap = Nothing
Set pAV = Nothing
Set pCenterPoint = Nothing
Set pConstructCircleArc = Nothing
Set pSegmentCollection = Nothing
Set pPolygon = Nothing
Set pGraphContainer = Nothing
Set pElement = Nothing
Set pFillShpElem = Nothing
Set pSFSymbol = Nothing
Set pColor = Nothing
Set pLineColor = Nothing
Set pLineSymbol = Nothing
Set pPCS = Nothing
Exit Sub
EH:
MsgBox Err.Number & " " & Err.Description
End Sub
Public Function ConvertUnits(inUnits As Double) As Double
On Error GoTo EH
Dim pUI As IUnitConverter
Set pUI = New UnitConverter
ConvertUnits = pUI.ConvertUnits(inUnits, esriFeet, esriMeters)
Set pUI = Nothing
Exit Function
EH:
MsgBox Err.Number & " " & Err.Description, , "ConvertUnits"
End Function
Public Function ProjectToWGSAzimuthal(ByVal dLon As Double, _
ByVal dLat As Double) As IProjectedCoordinateSystem2
Dim pSRF As ISpatialReferenceFactory2
Set pSRF = New SpatialReferenceEnvironment
Set ProjectToWGSAzimuthal = pSRF.CreateProjectedCoordinateSystem(esriSRProjCS_WGS1984N_PoleAziEqui)
ProjectToWGSAzimuthal.CentralMeridian(True) = dLon
ProjectToWGSAzimuthal.LatitudeOfOrigin = dLat
Set pSRF = Nothing
End Function