I have recently bought a goat for sacrifice but at morning i saw it crippled from back leg ... I checked it thoroughly and there was no visible mark of any injury but i believe it may have got rope strangled between its toe... so it is reluctant to put his back leg on floor while walking ...but sometimes he plunges on a leafy tree but sometimes takes its leg off from the ground.. As Eid is ahead so I am not sure if its ready for sacrifice or not?
According to fatwa islamweb #7297: The majority of scholars say if you bought cattle with the intention of sacrifice and it was sane from any visible deficiency (that would be considered as a cause to declare sacrifice with such a cattle as invalid), at the time of acquisition. Even if such a deficiency (not an illness!) appeared later the sacrifice would still be valid.
Ibn Qudamah (hanbali scholar) said in his al-Mughni المغني:
In the following I'll translate from Arabic language, as this translation is of my own take it with the necessary care!
وَلَوْ أَوْجَبَهَا سَلِيمَةً ، فَعَابَتْ عِنْدَهُ ، ذَبَحَهَا ، وَكَانَتْ أُضْحِيَّةً
And if a person bought a sane sacrifice, and it got defective later, he could duct it and it would count as a sacrifice.
وَجُمْلَتُهُ أَنَّهُ إذَا أَوْجَبَ أُضْحِيَّةً صَحِيحَةً سَلِيمَةً مِنْ الْعُيُوبِ ، ثُمَّ حَدَثَ بِهَا عَيْبٌ يَمْنَعُ الْإِجْزَاءَ ، ذَبَحَهَا ، وَأَجْزَأَتْهُ . رُوِيَ هَذَا عَنْ عَطَاءٍ ، وَالْحَسَنِ ، وَالنَّخَعِيِّ ، وَالزُّهْرِيِّ ، وَالثَّوْرِيِّ ، وَمَالِكٍ ، وَالشَّافِعِيِّ ، وَإِسْحَاقَ .
This means if one bought a sane non defective cattle for sacrifice, which became latter defective in a way that would count as invalidating sacrifice, he could slaughter it and his sacrifice is valid. This (view) was held by 'Ata', al-Hassan, An-Nakha'y, az-Zuhri, a-Thawry, Malik, a-Shafi'y and Ishaaq.
وَقَالَ أَصْحَابُ الرَّأْيِ : لَا تُجْزِئْهُ ; لِأَنَّ الْأُضْحِيَّةَ عِنْدَهُمْ وَاجِبَةٌ ، فَلَا يَبْرَأُ مِنْهَا إلَّا بِإِرَاقَةِ دَمِهَا سَلِيمَةً ،
While the companions of Ra'y said it wouldn't count as valid. This is because the sacrifice (udhiyyah) is considered as wajib by them. And wouldn't count as valid according to their view unless it was offered in a sane (from any deficiency) state.
This means that the hanafi view is not going a long with the majority view and requires a sane cattle at the time of sacrifice, not at the time of acquisition. In case you are following the hanafi view: You may need to check whether the actual deficiency is an injury or broken leg, an injury might not be regarded as a deficiency invalidating the sacrifice (not sure about the hanafi view), while a broken leg surely will!
As for the main evidence of the majority view you may find:
“We bought a ram for sacrifice, then a wolf tore some flesh from its rump and ears. We asked the Prophet (ﷺ) and he told us to offer it as a sacrifice.”
(Sunan ibn Majah)
Note that if the deficiency turned into a visible illness the majority view is that a sacrifice with such an animal would be regarded as invalid.