ven figure shows twohe gi parallelgents XY and X'Y'at the points A and

1.	ven figure shows twohe gi parallelgents XY and X'Y'at the points A and Brespectively to the creleith centre OAnother tangent CD is drawn parallel to ABat the point P. Show that a circle with P ascentre and OP as radius will pass throughCand D
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

ven figure shows twohe gi parallelgents XY and X'Y'at the points A and Brespectively to the creleith centre OAnother tangent CD is drawn parallel to ABat the point P. Show that a circle with P ascentre and OP as radius will pass throughCand D

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