Circles: Exercise 10.1 Video Lecture | Mathematics (Maths) Class 10

0:0:0: I am sure you all have seen a tire and
0:0:3: know what shape it is yes it is a
0:0:7: circle here in this video we will study
0:0:10: about the parts of a circle and an
0:0:12: important theorem from chapter 10 and do
0:0:14: exercise
0:0:16: 10.1 first let's start by learning about
0:0:19: various parts of a circle here we have a
0:0:23: circle this point is called the center
0:0:26: of the circle the constant distance from
0:0:29: the center of the circle and any point
0:0:31: on the circle is called radius a line
0:0:34: segment joining any two points on a
0:0:36: circle is called code a line segment
0:0:39: which passes through the center of the
0:0:41: circle and its end points are on the
0:0:43: circle is called
0:0:45: diameter the length of the outer
0:0:47: boundary of a circle is called its
0:0:50: circumference any part or segment of the
0:0:53: circumference or outer boundary of the
0:0:55: circle is called an arc a sector of a
0:0:58: circle is a portion or part of a circle
0:1:1: that is composed of an ark and its two
0:1:3: radi a segment of a circle can be
0:1:6: defined as a region bounded by a chord
0:1:9: and a corresponding Arc lying between
0:1:11: the Cordes and
0:1:13: points let us now examine the different
0:1:15: situations that can arise when a circle
0:1:18: and a line are given in a plane so let
0:1:21: us consider a circle and a line a in
0:1:25: this picture the line ab and the circle
0:1:27: do not have any common points
0:1:30: so in this case AB will be called a
0:1:33: non-intersecting line with respect to
0:1:35: the circle what do you think about this
0:1:39: picture yes in this the line AB is
0:1:42: intersecting The Circle at two points
0:1:44: and is called the secant of the circle
0:1:46: and lastly in this the line ab and the
0:1:49: circle have only one point in common and
0:1:52: is called a tangent to the
0:1:54: circle next we are going to study and
0:1:57: prove the theorem
0:1:58: 10.1 the theorem states that the tangent
0:2:2: at any point of a circle is
0:2:4: perpendicular to the radius through the
0:2:6: point of
0:2:7: contact now let us prove the statement
0:2:9: of the theorem we are given a circle
0:2:12: with Center o and a tangent XY to The
0:2:15: Circle at a point P we need to prove
0:2:18: that op is perpendicular to XY take a
0:2:22: point Q on XY other than p and join o q
0:2:27: the point Q must lie outside the circle
0:2:31: why because if Q lies inside the circle
0:2:34: XY will become a secant and not a
0:2:37: tangent to the circle o q has a point on
0:2:40: the circle Also let's name it R o r is
0:2:45: also the radius of the
0:2:47: circle this means o r is equal to op and
0:2:50: o r is less than o q this implies that
0:2:54: op is less than o
0:2:56: q since this happens for every point on
0:2:59: the line L XY except the point P op is
0:3:3: the shortest of all the distances from
0:3:5: point O to the points of XY according to
0:3:8: shortest distance theorem the
0:3:10: perpendicular distance is the shortest
0:3:12: distance between a point and a
0:3:15: line so op is perpendicular to
0:3:19: XY hence
0:3:21: proved by this theorem we can also
0:3:24: conclude that at any point on a circle
0:3:26: there can be one and only one tangent
0:3:29: and and the line containing the radius
0:3:31: through the point of contact is also
0:3:33: sometimes called the normal to the
0:3:35: circle at the point now let's start the
0:3:39: exercise 10.1 from
0:3:41: ncert the first question is how many
0:3:45: tangents can a circle have think about
0:3:48: it
0:3:49: yourself yes the answer is infinite
0:3:53: because we have studied that there are
0:3:55: infinite number of points on the
0:3:57: boundary of a circle and each point can
0:3:59: have have a different tangent passing
0:4:1: through it hence there can be infinite
0:4:4: number of
0:4:5: tangents question two is fill in the
0:4:9: blanks a tangent to a circle intersects
0:4:12: it in dash Point or points what do you
0:4:15: think will fill the
0:4:17: blank yes the answer is one a tangent to
0:4:21: a circle intersects it in one
0:4:24: point a line intersecting a circle in
0:4:26: two points is called a dash think for
0:4:30: yourself yes the answer is secant a line
0:4:34: intersecting a circle in two points is
0:4:36: called a
0:4:38: secant a circle can have Dash parallel
0:4:40: tangents at the most how many do you
0:4:44: think they are yes it is two a circle
0:4:48: can have two parallel tangents at the
0:4:51: most the common point of a tangent to a
0:4:54: circle and the circle is called Dash try
0:4:58: once yes
0:5:0: it is called the point of contact the
0:5:3: common point of a tangent to a circle
0:5:5: and the circle is called the point of
0:5:8: contact the next question is a tangent
0:5:12: PQ at a point P of a circle of radius 5
0:5:14: cm meets a line through the center o at
0:5:17: a point Q so that o q is equal to 12
0:5:20: CM what is the length
0:5:23: PQ let's make the circle of radius 5 cm
0:5:27: and Center o all Al construct a tangent
0:5:31: PQ we know that the length of op is
0:5:34: equal to the radius which is 5
0:5:37: cm also we know that the length oq is
0:5:40: equal to 12
0:5:42: CM using the theorem we studied which
0:5:45: states that the tangent at any point of
0:5:47: a circle is perpendicular to the radius
0:5:50: through the point of
0:5:51: contact so angle opq is equal to
0:5:55: 90° so we have a right angle triangle op
0:6:0: PQ using Pythagoras Theorem we can write
0:6:4: PQ ² is equal to oq s- op s PQ ² is = to
0:6:11: 12 s - 5 S = to 144 -
0:6:17: 25 hence we get PQ equal to under < TK
0:6:21: 119
0:6:22: CM so the last question is draw a circle
0:6:27: and two lines parallel to a given line
0:6:29: such that one is a tangent and the other
0:6:32: is a secant to the circle let's draw
0:6:36: first a circle then a reference line now
0:6:40: we have to draw a line which is parallel
0:6:42: to this reference line and is tangent to
0:6:45: the circle here it is and lastly we have
0:6:49: to draw a secant to the circle which is
0:6:51: also parallel to the reference line we
0:6:54: hope that you have understood the
0:6:56: concept of
0:6:57: circles now here's a secret on how you
0:7:0: can study effectively with the urv app
0:7:3: you can learn with chapter notes watch
0:7:6: video lectures and solve insert based
0:7:8: McQ tests of this chapter on
0:7:11: urv and that's not all you also get
0:7:14: amazing courses for class 10 and much
0:7:16: more for your class 10
0:7:18: preparation thank
0:7:28: you