Here's another circuit from Electronics For You, an Indian publication. It appears to be correct, until you see the 100R resistor charging the battery.
The transformer is 0-12v AC and this will produce a DC voltage at least 18v-20v after rectification, on no load or when powering the alarm during normal conditions. (It could be as high as 22v).
This voltage is far too high for a 12v battery and it will cause gassing and the battery will dry out in a few months.
It is absolutely essential to charge the battery until its voltage reaches 14.1volts then turn-off the charging voltage so that the battery does not produce bubbles. This circuit does not do that.