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middle aligning a div inside another div with middle alligned content

I have two divs, one inside another and the inner div has ap tag which has aligned middle. markup is

<div class="box1">
    <div class="box2">
        <p>hello</p>
    </div>
</div>

style rules are

.box1 {
    width: 400px;
    height: 400px;  
    background: red;
    text-align: center;
}
.box2 {
    display: table-cell;
    width: 200px;
    height: 200px; 
    margin: auto;
    vertical-align: middle; 
    text-align: center;   
    background: yellow;
}

What i am trying to do is centering the p tag vertically and horizontally inside the inner div(box2) and centering the inner div vertically and horizontall insde the outer div (box1). i failed to center the inner div(box2) inside the outer div. Please help me to do it. i have created a fiddle for this -> http://jsfiddle.net/64WAW/1/

Please look at this:

http://jsfiddle.net/itz2k13/64WAW/2/

.box1 {
 display: table-cell;
 width: 400px;
 height: 400px;  
 background: red;
 text-align: center;
 vertical-align: middle;
}

.box2 {    
 width: 200px;
 height: 200px; 
 background: yellow;
 margin: auto;
 line-height: 200px;
}

HTML:

<div class="box1">
    <div class="box2container">
        <div class="box2">
            <p>hello</p>
        </div>
    </div>
</div>

Css:

.box1 {
    width: 400px;
    height: 400px;  
    background: red;
    text-align: center;
}
.box2 {
    position:relative;
    top:-50%;
    left:-50%;
    width: 200px;
    height: 200px; 
    background: yellow;
    line-height:200px;
}

.box2container{
    width: 200px;
    height: 200px; 
    position:relative;
    top:50%;
    left:50%;
}

This solution avoid using display:table-cell which is not supported by older browsers. Check out the fiddle

you will use flexbox, it is easy.it is like this:

.box1,
.box2{
  display: -moz-box; /*Safari,  iOS, Android browser, older WebKit browsers. */
  display: -webkit-box;/* Firefox (buggy) */
  display: -ms-flexbox; /*IE 10*/
  display: -webkit-flex;/*Chrome 21+ */
  display: flex;/*Opera 12.1, Firefox 22+ */

  -webkit-box-align: center; 
  -moz-box-align: center;
  -ms-flex-align: center; 
  -webkit-align-items: center;
  align-items: center;
  -webkit-box-pack: center; 
  -moz-box-pack: center; 
  -ms-flex-pack: center; 
  -webkit-justify-content: center;
  justify-content: center;
}
.box1{
    width: 400px;
    height: 400px;  
    background: red;
    text-align: center;     
}
.box2 {
    background: yellow;
    width: 200px;
    height: 200px;
}

pls view the demo ,Detail please see the tutorial

use the display:inline-block and add :after for it parent container:

.box1 {
    width: 400px;
    height: 400px;  
    background: red;
    text-align: center;
}
.box2 {
    display: inline-block;
    width: 200px;
    height: 200px; 
    vertical-align: middle; 
    text-align: center;   
    background: yellow;
}
.box1:after {
  content:"";
  width: 1px;
  height: 100%;
  position: relative;
  display: inline-block;
  vertical-align: middle; 
}

the demo

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