A turbomachine component, comprising: a turbine blade, which is rotatable about a rotor of a turbine for power generation operations; and a platform with which the turbine blade is to be assembled, the turbine blade being formed to define a main circuit having a circumferential appendage and the platform being formed to define: a platform circuit, and a substantially radially extendible pathway configured to be coupled to the appendage and to the platform circuit, wherein the appendage extends circumferentially from the main circuit and is formed with radial tapering or curvature, wherein the appendage comprises: a radially outward side, which is configured to be disposed proximate to the platform circuit, and which is configured with relatively shallow tapering or curvature relative to the deep tapering or curvature, and a radially inward side, which is distant from the platform circuit, and which is configured with relatively deep tapering or curvature relative to the shallow tapering or curvature, characterized in that the platform circuit extends axially through the platform, including one or more platform cavities, and the pathway is formed in the platform; wherein the appendage is extended to intersect with the pathway at a location that is radially inward from or underneath any of the one or more of the platform cavities; wherein the pathway meets the platform cooling circuit at an intersection; and wherein the turbomachine component further comprises a plug to prevent leakage from a radially inward section of the pathway. a turbine blade, which is rotatable about a rotor of a turbine for power generation operations; and a platform with which the turbine blade is to be assembled, the turbine blade being formed to define a main circuit having a circumferential appendage and the platform being formed to define: a platform circuit, and a substantially radially extendible pathway configured to be coupled to the appendage and to the platform circuit, wherein the appendage extends circumferentially from the main circuit and is formed with radial tapering or curvature, wherein the appendage comprises: a radially outward side, which is configured to be disposed proximate to the platform circuit, and which is configured with relatively shallow tapering or curvature relative to the deep tapering or curvature, and a radially inward side, which is distant from the platform circuit, and which is configured with relatively deep tapering or curvature relative to the shallow tapering or curvature, characterized in that the platform circuit extends axially through the platform, including one or more platform cavities, and the pathway is formed in the platform; wherein the appendage is extended to intersect with the pathway at a location that is radially inward from or underneath any of the one or more of the platform cavities; wherein the pathway meets the platform cooling circuit at an intersection; and wherein the turbomachine component further comprises a plug to prevent leakage from a radially inward section of the pathway. a platform circuit, and a substantially radially extendible pathway configured to be coupled to the appendage and to the platform circuit, wherein the appendage extends circumferentially from the main circuit and is formed with radial tapering or curvature, wherein the appendage comprises: a radially outward side, which is configured to be disposed proximate to the platform circuit, and which is configured with relatively shallow tapering or curvature relative to the deep tapering or curvature, and a radially inward side, which is distant from the platform circuit, and which is configured with relatively deep tapering or curvature relative to the shallow tapering or curvature, characterized in that the platform circuit extends axially through the platform, including one or more platform cavities, and the pathway is formed in the platform; wherein the appendage is extended to intersect with the pathway at a location that is radially inward from or underneath any of the one or more of the platform cavities; wherein the pathway meets the platform cooling circuit at an intersection; and wherein the turbomachine component further comprises a plug to prevent leakage from a radially inward section of the pathway. a radially outward side, which is configured to be disposed proximate to the platform circuit, and which is configured with relatively shallow tapering or curvature relative to the deep tapering or curvature, and a radially inward side, which is distant from the platform circuit, and which is configured with relatively deep tapering or curvature relative to the shallow tapering or curvature, characterized in that the platform circuit extends axially through the platform, including one or more platform cavities, and the pathway is formed in the platform; wherein the appendage is extended to intersect with the pathway at a location that is radially inward from or underneath any of the one or more of the platform cavities; wherein the pathway meets the platform cooling circuit at an intersection; and wherein the turbomachine component further comprises a plug to prevent leakage from a radially inward section of the pathway.