R S AGGARWAL AND V AGGARWAL Solutions for Class 10 Maths Chapter 8 - Circles
Chapter 12 - Circles MCQ
Correct option : (b)
We can draw only 2 tangents from an external point to a circle.
Correct option: (d)
The diameter of the circle always passes through the centre. This means all the diameters of a given circle will intersect at the centre, and hence they cannot be parallel.
Correct option: (d)
Options (a), (b) and (c) are all true.
However, option (d) is false since we can draw only parallel tangents on either side of the diameter, which would be parallel to a given line.
Correct option: (d)
Options (a), (b) and (c) are all true.
However, option (d) is false since a straight line can meet a circle at two points even as shown below.
Correct option: (d)
Options (a), (b) and (c) are true.
However, option (d) is false since it is not possible to draw a tangent from a point inside a circle.
Chapter 12 - Circles Ex. 8A
PA is the tangent to the circle with center O and radius AO = 8 cm. The point P is at a distance of 17 cm from O.
In PAO,
A = 90
By Pythagoras theorem:
Hence, the length of the tangent = 15 cm.
PA is the tangent to the circle with centre O and radius, such that PO = 25 cm, PA = 24 cm
In PAO,
A = 90,
By Pythagoras theorem:
Hence, the radius of the circle is 7 cm.
Given AP is a tangent at A and OA is radius through A and PA and PB are the tangent segments to circle with centre O.
Therefore, OA is perpendicular to AP, similarly, OB is perpendicular to BP.
OAP = 90
And OBP = 90
So, OAP =
OBP = 90
OBP +
OAP = (90 + 90) = 180
Thus, the sum of opposite angles of quad. AOBP is 180
AOBP is a cyclic quadrilateral
Given: From an external point P, tangent PA and PB are drawn to a circle with centre O. CD is the tangent to the circle at a point E and PA = 14cm.
Since the tangents from an external point are equal, we have
PA = PB,
Also, CA = CE and DB = DE
Perimeter of PCD = PC + CD + PD
=(PA - CA) + (CE + DE) +(PB - DB)
= (PA - CE) + (CE + DE) + (PB - DE)
= (PA + PB) = 2PA = (2 14) cm
= 28 cm
Hence, Perimeter of PCD = 28 cm
A circle is inscribed in a triangle ABC touching AB, BC and CA at P, Q and R respectively.
Also, AB = 10 cm, AR = 7cm, CR = 5cm
AR, AP are the tangents to the circle
AP = AR = 7cm
AB = 10 cm
BP = AB - AP = (10 - 7)= 3 cm
Also, BP and BQ are tangents to the circle
BP = BQ = 3 cm
Further, CQ and CR are tangents to the circle
CQ = CR = 5cm
BC = BQ + CQ = (3 + 5) cm = 8 cm
Hence, BC = 8 cm
Let the circle touches the sides AB, BC, CD and DA at P, Q, R, S respectively
We know that the length of tangents drawn from an exterior point to a circle are equal
AP = AS ----(1) {tangents from A}
BP = BQ ---(2) {tangents from B}
CR = CQ ---(3) {tangents from C}
DR = DS----(4) {tangents from D}
Adding (1), (2) and (3) we get
AP + BP + CR + DR = AS + BQ + CQ + DS
(AP + BP) + (CR + DR) = (AS + DS) + (BQ + CQ)
AB + CD = AD + BC
AD = (AB + CD) - BC = {(6 + 4) - 7} cm = 3 cm
Hence, AD = 3 cm
Given O is the centre of two concentric circles of radii 4 cm and 6 cm respectively. PA and PB are tangents to the outer and inner circle respectively. PA = 10cm. Join OA, OB and OP.
Then, OB = 4 cm, OA= 6 cm and PA = 10 cm
In triangle OAP,
Hence, BP = 10.9 cm
Chapter 12 - Circles Ex. 8B
Chapter 12 - Circles FA
- A line intersecting a circle in two distinct points is called a secant.
- A circle can have two parallel tangents at the most.
- This is since we can draw only parallel tangents on either side of a diameter.
- The common point of a tangent to a circle and the circle is called the point of contact.
- A circle can have infinitely many tangents.
Other Chapters for CBSE Class 10 Maths
Chapter 1- Real Numbers Chapter 2- Polynomials Chapter 3- Linear equations in two variables Chapter 4- Quadratic Equations Chapter 5- Arithmetic Progressions Chapter 6- Co-ordinate Geometry Chapter 7- Triangles Chapter 9- Constructions Chapter 10- Trigonometric Ratios Chapter 11- T-Ratios of Some Particular Angles Chapter 12- Trigonometric Ratios of Complementary Angles Chapter 13- Trigonometric Identities Chapter 14- Height and Distance Chapter 15- Perimeter and Areas of Plane Figures Chapter 16- Areas of Circle, Sector and Segment Chapter 17- Volume and Surface Areas of Solids Chapter 18- Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive Chapter 19- ProbabilityR S AGGARWAL AND V AGGARWAL Solutions for CBSE Class 10 Subjects
Kindly Sign up for a personalised experience
- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions
Sign Up
Verify mobile number
Enter the OTP sent to your number
Change