Question

The two circles with centres P and R touch each other externally at 0. A line passing through O cut the circles at T and S respectively. Then
(1)PT and RS are of equal length
(2) PT and RS are perpendicular to each
other
(3) PT and RS are interesting to each other
(4) PT and RS are parallel.​

Answer 1

PT ║ SR  (PT and RS are parallel.) if The two circles with centers P and R touch each other externally at Out the circles at T and S respectively.

Step-by-step explanation:

∠POT  = ∠ROS  ( opposite angles)

now in Δ POT  

PO = PT  ( Radius)

=> ∠POT = ∠PTO

& in Δ ROS

RO = RS  ( Radius)

=> ∠ROS  = ∠OSR

now as ∠POT  = ∠ROS  

=>  ∠PTO = ∠OSR

=> PT ║ SR

PT = RS  (only if radius of both circles are equal)

Learn more about tangents:

The sum of the lengths of two opposite sides of

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TA and TB are the tangents to the circle with center O

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Answer 2

Option (4)

PT and RS are parallel.​

Step-by-step explanation:

given that

The two circles with centres P and R touch each other externally at 0. A line passing through O cut the circles at T and S respectively.

then ,

∠POT  = ∠ROS  ( opposite angles )

PO = PT  ( Radius)

∠POT = ∠PTO

& in Δ ROS

RO = RS  ( Radius)

∠ROS  = ∠OSR

therefore

PT is parallel to RS .

hence ,

option (4)  PT and RS are parallel.​

#Learn more:

A ciircle centered at P with radius 4cm and another circle centered at Q with radius 16cm touch each other externally .A third circle with centre R is drawn to touch the first two circles and one of their common internal tangents is drawn Then find R

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