Let $$\mathcal {S}^*_C$$ S C ∗ be the class of normalized analytic functions f in the unit disc with $$zf'(z)/f(z)$$ z f ′ ( z ) / f ( z ) lying in the region bounded by the cardioid given by the equation $$(9 x^2+9 y^2-18x+5)^2- 16 (9 x^2+9 y^2-6x+1)=0$$ ( 9 x 2 + 9 y 2 - 18 x + 5 ) 2 - 16 ( 9 x 2 + 9 y 2 - 6 x + 1 ) = 0 . We determine the structural formula, coefficient estimates, growth results and various radii constants such as the radius of starlikeness, radius of lemniscate of Bernoulli starlikeness, radius of M-starlikeness and radius of $$\mathcal {M}(\beta )$$ M ( β ) -starlikeness for functions in the class $$\mathcal {S}^*_C$$ S C ∗ . In addition, the $$\mathcal {S}^*_C$$ S C ∗ -radii for functions belonging to several interesting classes are determined. All the results obtained are sharp.