In Figure, common tangents $P Q$ and $R S$ to two circles intersect at $A$ . Prove that $P Q = R S .$

Open in App

Solution

From figure

$A$ is point from which $2$ tangents are drawn at both circles.

$\Rightarrow P A = R A$ $\to (a)$ , $A S = A Q$ $\to (b)$ ........... ( $∵$ tangents drawn from a outside point to a circle are equal)

Now add $(a)$ & $(b)$

$\Rightarrow P A + A S = R A + A Q$

or, $P A + A Q = R A + A S$

$\Rightarrow P Q = R S$

Suggest Corrections

Similar questions

In the given figure, two circles intersect each other at the points A & B. If PQ & PR are tangents to circles at point P and BA is extended to meet at P, prove PQ = PR

Q. If figure common tangents AB and CD to two circles intersect at E. Prove that AB = CD.

Q. In the given figure two circles intersect each other in points A and B.Two tangents touch these circles in points P,Q and R,S as shown.line AB intersects seg PQ in C and seg RS in D.Show that C and D are the mid points of seg PQ and seg RS respectively.

Q. In the given figure, two circles intersect each other at points S and R. Their common tangent PQ touches the circle at points P, Q. Prove that,

∠ P R Q + ∠ P S Q = 180^{o}

Q. Two circles with centres

M

and

N

intersect each other at

P

and

Q

. The tangents drawn from point

R

on the line

P Q

touch the circles at

S

and

T

. Prove that,

R S = R T

Join BYJU'S Learning Program

In Figure, common tangents PQ and RS to two circles intersect at A. Prove that PQ=RS.

From figureA is point from which 2 tangents are drawn at both circles.⇒PA=RA →(a), AS=AQ →(b)........... (∵ tangents drawn from a outside point to a circle are equal)Now add (a) & (b)⇒PA+AS=RA+AQor, PA+AQ=RA+AS⇒PQ=RS

In Figure, common tangents $P Q$ and $R S$ to two circles intersect at $A$ . Prove that $P Q = R S .$