What is the distance be the two tangents of circle of radius 6cm
Answers
Answered by
0
equal to diameter.
which is 12cm.
which is 12cm.
Answered by
0
it cannot be answered directly that ans is 12. So,by tangent segment theorem,
tangent at any point is perpendicular with the radius at point of contact.
therefore both of them would be perpendicular at the points of contact.so we should consider point of contact A and B of t1(tangent 1) and t2(tangent 2) respectively.Consider the centre as O. and take points c on t1 and d on t2.therefore <OAC+<OBD=
=90°+90°=180°,it means <OAC and <OBD are interior angles and by interior angles test those two tangents are parallel.Draw a line passing through centre O of circle parallel to both tangents.take point P on it
hence <AOP and <BOP are 90°
this means they are linear pair 90°+90°=180°
therefore points A,O,B are collinear.
therefore distance between tangents is 2×radius as AB is diameter
=2×6=12.
tangent at any point is perpendicular with the radius at point of contact.
therefore both of them would be perpendicular at the points of contact.so we should consider point of contact A and B of t1(tangent 1) and t2(tangent 2) respectively.Consider the centre as O. and take points c on t1 and d on t2.therefore <OAC+<OBD=
=90°+90°=180°,it means <OAC and <OBD are interior angles and by interior angles test those two tangents are parallel.Draw a line passing through centre O of circle parallel to both tangents.take point P on it
hence <AOP and <BOP are 90°
this means they are linear pair 90°+90°=180°
therefore points A,O,B are collinear.
therefore distance between tangents is 2×radius as AB is diameter
=2×6=12.
Attachments:
Similar questions