Question

prove that the length of tangents drawn from an external point to a circle are equal

Answer 1

To prove:-
PT=QT
Let us consider OPT and OQT 
OP=OQ
∠OPT=∠OQT=90°
 Hence by RHS the triangles are equal 
Thus,PT=QT
Hence verified

Hope this helps you!!

Answer 2

Hi friend here is Brainly star Roman1111 reporting in and here is your answer

Given: A circle with centre O; PA and PB are two tangents to the circle drawn from an external point P.

To prove: PA = PB

Construction: Join OA, OB, and OP.




It is known that a tangent at any point of a circle is perpendicular to the radius through the point of contact.

OA perpendicular PA and OB perpendicular PB ... (1)

In triangle OPA and triangle OPB:

Angle OAP = angle OBP (Using (1))

OA = OB (Radii of the same circle)

OP = OP (Common side)

Therefore, triangle OPA triangle OPB (RHS congruency criterion)

PA = PB

(Corresponding parts of congruent triangles are equal)

Thus, it is proved that the lengths of the two tangents drawn from an external point to a circle are equal.


Hope it helps you.............!!