Intersection probabilities for a chordal SLE path and a semicircle

We drive a number if estimates for the probability that a chordal SLE kappa path in the upper half plane H intersects a semicircle centred on the real line. We prove that if 0 < kappa < 8 and gamma: [0, infinity) -> (H) over bar is a chordal SLE kappa is H from 0 to infinity, then P{gamma[0, infinity) boolean AND c(x; rx) not equal 0} asymptotic to r(4a-1) where a = 2/kappa and C(x; rx) denotes the semicircle centred at x > 0 of radius rx, 0 < r <= 1/3, in the upper half plane. As an application of our results, for 0 < kappa < 8, we derive an estimate for the diameter of a chordal SLE kappa path in H between two real boundary points 0 and x > 0. For 4 < kappa < 8, we also estimated the probability that an entire semicircle on the real line is swallowed at once by a choral SLE kappa path in H from 0 to infinity.