Question

prove that if two circles touch each other the centre and point of contact are collinear

Answer 1

Step
Statement
Reason

1
AT=BT
TA and TB are tangents from an external point T
2
TAB=TBA
2 sides are equal
3
PT=QT
TP and TQ are tangents from an external point T
4
TPQ=TQP
2 sides are equal
5
ATB= 1800- (TAB+TBA)=
1800- 2TAB
InTAB, sum of all the angles = 1800
6
ATB= 1800- (TPQ+TQP)=
1800- 2TPQ
InTPQ, sum of all the angles = 1800
7
TAB =TPQ
Equate RHS of steps 5, 6
8
TAB =TPQ=TQP =TBA
Steps 7, 4, 2
9
TAB ||| TPQ
Triangles