Question

I will mark brainliest plzz urgent..If PAB is secant and PT is tangent then prove tht PAxPB=PT^2

Answer 1

Hello! dear,

Your answer goes like this .....

First Join point T to point A to point B.

Now you can observe two triangles by Joining the lines :First triangle:PTA AND PBT 

Also remember that :Angle between a chord and a tangent at the point of contact =Angle,Subtended by the same chord,At any point but in opposite segment.

TA is a secant whereas,TP is a tangent.
Therefore,angle PTA{angle between tangent and chord}
=angle TBA {angle in the opposite segment} ------------{1}

angle PTA =angle TBP  --------------------------{2}

angle PTA in triangle PTA=angle TBA in triangle PBT{from[1]above} ---3
angle TPA in triangle PTA=angle TPB in trianlge PBT {common angle}---4

From {3} and {4},Two angles of triangles of triangles PTA and PBT are equal.
Hence triangles PTA and PBT are similar.

Therefore,PT/PB=PA/PT {or} PT²=PAXPB.


Thank you dear,

Hope It helps.

Answer 2

HELLO....

QUESTION :- If PAB is secant and PT is tangent then prove tht PAxPB=PT^2