How to limit transform.translate inside a sphere

Question

I have sphere named Pointer that can move everywhere with transform.Translate() but i want this sphere can only move inside a half-sphere named LimitSphere, i don't know how to do it.

i already tried to use Mathf.Clamp but as you can see on this image

but when i set an inscribed square i loose too much space (yellow)
and when i set an circumscribed square there is too much space out of the circle (purple/pink)

So is there any solution to limit a movement inside sphere ?

EDIT : That's my actual code :

using UnityEngine;
using System.Collections;

public class TranslationClavier : MonoBehaviour {

    public float vitesse_translation = 1.0f;



    void Update () {
            if (Input.GetKey(KeyCode.DownArrow))
            {
                transform.Translate(Vector3.up * vitesse_translation * Time.deltaTime);
            }

            if (Input.GetKey(KeyCode.UpArrow))
            {
                transform.Translate(Vector3.down * vitesse_translation * Time.deltaTime);
            }

            if (Input.GetKey(KeyCode.RightArrow))
            {
                transform.Translate(Vector3.right * vitesse_translation * Time.deltaTime);
            }

            if (Input.GetKey(KeyCode.LeftArrow))
            {
                transform.Translate(Vector3.left * vitesse_translation * Time.deltaTime);
            }

            if (Input.GetKey(KeyCode.I))
            {
                transform.Translate(Vector3.forward * vitesse_translation * Time.deltaTime);
            }

            if (Input.GetKey(KeyCode.K))
            {
                transform.Translate(-Vector3.forward * vitesse_translation * Time.deltaTime);
            }
    }

}

under you can see my little sphere and i want to clamp her inside the big sphere collider

Answer 1

i finally did this

    // Get the new position for the object.
    Vector3 movement = new Vector3(Input.GetAxis("Vertical"), Input.GetAxis("VerticalJD"), Input.GetAxis("Horizontal")) * vitesse_translation;
    Vector3 newPos = transform.position + movement;

    // Calculate the distance of the new position from the center point. Keep the direction
    // the same but clamp the length to the specified radius.
    Vector3 offset = newPos - centerPt;
    transform.position = (centerPt + Vector3.ClampMagnitude(offset, radius));