theorm9.2 of class 10
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The lengths of tangents drawn from an external point to a circle are equal.
Given : A circle with centre O. is a point lying outside the circle and PA and PB are two
angents to the circle from P
to prove PA=PB
proof: Join OA, OB and OP
20AP - OBP=90°
Now in the two right triangles
AOAP and AOBP
OA =OB radii of same circle)
OP =OP (Common)
Therfore, By R.H.S. Congruenc
OAP =OBP
This gives PA=PB
Hence Proved.
Given : A circle with centre O. is a point lying outside the circle and PA and PB are two
angents to the circle from P
to prove PA=PB
proof: Join OA, OB and OP
20AP - OBP=90°
Now in the two right triangles
AOAP and AOBP
OA =OB radii of same circle)
OP =OP (Common)
Therfore, By R.H.S. Congruenc
OAP =OBP
This gives PA=PB
Hence Proved.
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