Magento 1.9 Product Review – How to Add Captcha to Reviews

I need to put a captcha on the product review feature to prevent spams. Unfortunately it doesn't work. The captcha doesn't appear on the page, even if I did the same for the contact page and it works …

Here some sample of my code…

app/design/frontend/default/MyTheme/MyCompany/MyModule/catalog.xml:

<catalog_product_view translate="label">
    <reference name="content">
        <block type="review/form" name="product.info.review.form" as="info_review_form" template="review/form.phtml">
            <block type="core/text_list" name="review.form.additional.info">
                <block type="captcha/captcha" name="captcha">
                    <reference name="head">
                        <action method="addJs"><file>mage/captcha.js</file></action>
                    </reference>
                    <action method="setFormId"><formId>review_form</formId></action>
                    <action method="setImgWidth"><width>230</width></action>
                    <action method="setImgHeight"><width>50</width></action>
                </block>
            </block>
        </block>
    </reference>
</catalog_product_view>

app/code/local/MyCompany/MyModule/etc/config.xml:

<?xml version="1.0"?>
<config>
    <modules>
        <MyCompany_MyModule>
            <version>0.0.0.1</version>
        </MyCompany_MyModule>
    </modules>
    <global>
        <models>
            <myModule>
                <class>MyCompany_MyModule_Model</class>
            </myModule>
        </models>
        <events>
            <controller_action_predispatch_contacts_index_post>
                <observers>
                    <myModule>
                        <class>myModule/observer</class>
                        <method>checkContactForm</method>
                    </myModule>
                </observers>
            </controller_action_predispatch_contacts_index_post>

            <controller_action_predispatch_udqa_index_post>
                <observers>
                    <myModule>
                        <class>myModule/observer</class>
                        <method>checkUdqaForm</method>
                    </myModule>
                </observers>
            </controller_action_predispatch_udqa_index_post>

            <controller_action_predispatch_review_product_post>
                <observers>
                    <myModule>
                        <class>myModule/observer</class>
                        <method>checkProductReviewForm</method>
                    </myModule>
                </observers>
            </controller_action_predispatch_review_product_post>
        </events>
    </global>
    <default>
        <captcha>
            <frontend>
                <areas>
                    <contacts>
                        <label>Contacts Page</label>
                    </contacts>
                    <udqa_question_form>
                        <label>Vendor Ask a Question</label>
                    </udqa_question_form>
                    <review_form>
                        <label>Product Review</label>
                    </review_form>
                </areas>
            </frontend>
        </captcha>
        <customer>
            <captcha>
                <always_for>
                    <contacts>1</contacts>
                    <udqa_question_form>1</udqa_question_form>
                    <review_form>1</review_form>
                </always_for>
            </captcha>
        </customer>
    </default>
</config>

My module is enabled in app/etc/modules/MyCompany_MyModule.xml
I've of course created the method checkProductReviewForm in the app/code/local/MyCompany/MyModule/Model/Observer.php

Please do NOT tell me to install a plugin like "Product Review reCaptcha" as I would like to use the core feature of Magento to do that, thank you.

Edit1: add bold on the last sentence to prevent other comments like Amit Bera's.