Reason : As TP is tangent and TBA is secant So TP2=TA×TB so, 82=TA×4⇒TA=16‌units as TA = 16 units so BA = 12 units Now in △ BTP,∠PBT=90° so by Pythagoras theorem TP2=TB2+BP2 ⇒ 82=42+BP2 ⇒ BP=4√3 ....(1) Now in Δ ABP,∠ABP=90°, so by Pythagoras theorem AP2=AB2+BP2 ⇒ 122+(4√3)2=(2r)2[As‌AP=2r] r=4√3‌units Hence option (1) is correct.