Question

find the distance between two parallel tangents of a circle of radius 3 cm ? plz ans me I will mark as brainlist with correct answer with steps ​

Answer 1

Answer:

So, AC || BD

We know, rangers is perpendicular to the radius at the point of contact.

So, angle OAC = angle OBD = 90

in quadrilateral ACDB,

AB|| CD

AC || BD

Angle BAC= 90

Hence, it is clear that Quadrilateral ACDB is a rectangle

So, angle C = angle D = 90

Now in quadrilateral OACP,

Angle A = 90

Angle C =90

Angle OPC = 90 and angle AOP = 90

This implies quadrilateral OACP is a rectangle.

So, OA = PC [ we know opposite sides are equal of rectangle]

similarly, quadrilateral OBDP is a rectangle

This implies OB = PD

Also OA = OB = OP [ theses are the radii of the same circles ]

So, PC = PD = OP

This implies , points O, C and D are equidistant from point ap

Hence, A circle with centre P and radius OP will pass through C and D