Dictionary Rank of a Word | Permutations & Combinations

 PERMUTATIONS & COMBINATIONS Rank of the word or Dictionary order of the English words like COMPUTER, COLLEGE, SUCCESS, SOCCER, RAIN, FATHER, etc. Dictionary Rank of a Word Method of finding the Rank (Dictionary Order) of the word  “R A I N” Given word: R A I N Total letters = 4 Letters in alphabetical order: A, I, N, R No. of words formed starting with A = 3! = 6 No. of words formed starting with I = 3! = 6 No. of words formed starting with N = 3! = 6 After N there is R which is required R ----- Required A ---- Required I ---- Required N ---- Required RAIN ----- 1 word   RANK OF THE WORD “R A I N” A….. = 3! = 6 I……. = 3! = 6 N….. = 3! = 6 R…A…I…N = 1 word 6 6 6 1 TOTAL 19 Rank of “R A I N” is 19 Method of finding the Rank (Dictionary Order) of the word  “F A T H E R” Given word is :  "F A T H E R" In alphabetical order: A, E, F, H, R, T Words beginni

Math Assignment Ch-10 Class X | Tangent to a circle


Tangent to a Circle

Maths assignment chapter 10 of class X. Maths assignment on tangent to the circle class 10th. Extra questions important for the CBSE examination for class X chapter 10.

Question 1
In the given figure the common tangents AB and CD to two circles intersect at E. Prove that AB = CD

Question 2
PT and PQ are two tangents from external point P. If ∠PQT = 70oFind ∠x
[Ans 20o]

Question 3
AB is the chord of the circle with centre O, AOC is the diameter and AT is the tangent at A.
Prove that . ∠1 = ∠2


Question 4

PQ and PR are tangents, SR ∥ PQ,  ∠P = 30o then,  Find ∠x        [Ans 30o]

Hint: RQP = PRQ  = 75o
RQP = S =  75o    ( Angles in the alternate segments are equal)
S + x + RQP = 180o

Question 5

CP, CQ and AB are three tangents to the circle. If CP = 11 cm, BR = 4 cm. Then
a) Find BC  [Ans 7 cm]
b) Prove that : CP = (1/2) ✕ Perimeter of  ABC
c) Find the perimeter of the   ABC  [Ans 22 cm]
d) Prove that : CA + AR = CB + BR
e) Prove that : AB = AP + BQ
f) If AC = 4 cm, AB = 5 cm, BC = 6 cm, then find CP  [Ans  7.5 cm]

Question 6
For the given figure answer the following questions
a) If AB = 10 cm, AR = 7 cm, and RC = 5 cm, find BC [Ans 8 cm]
b) If AB = 8 cm, BC = 10 cm, CA = 12 cm, then find AP, BQ and CR [Ans 7 cm, 5 cm, 3 cm]
c) If AB = 8 cm, BC = 7 cm, CA = 5 cm, find BQ [Ans 5 cm]
d) If AB = 8 cm, BC = 7 cm , CA = 5 cm, find the radius of the incircle [Ans √3]
e) If AB = AC then prove that BQ = CQ
Question 7
In △OPQ, OP =OQ = PQ = 6 cm, then find angle ∠PTQ

Question 8
In △ABC, AC = 8 cm, AB = 6 cm, ∠A = 90ofind the radius of the circle.
[Ans 2cm]

Question 9
PQ is the chord of length 6 cm of a circle of radius 6 cm, TP and TQ are tangents to the circle at point P and Q respectively. Find ∠PTQ. Also find the length TP.     
Ans [120o , TP = √12 cm]

Question 10
AP and BP are tangents. OA = 8 cm and OB = 5 cm. If AP = 15 cm, then find the length of BP.
 [Ans √264]




Question 11
In the given figure find the length of AB and AC
Ans [AB = 7.5, AC = 6.5 cm]

Question 12
∠D = 90o , BC = 38 cm, CD = 25 cm, and BP = 27 cm, find radius r of the circle.
[Ans 14 cm]

Question 13
O is the centre of the circle of radius 5 cm. T is a point such that OT = 13 cm and OT intersect the circle at E. If AB is the tangent to the circle at E, then find the length AB
 [Ans 20/3]
Hint :-        AT2  =  AE+ ET2
           (PT - AE)2  =  AE2  + ET2
             (12 - AE)2 = AE2 + 82
Question 14
A chord PQ of a circle is parallel to the tangent drawn at a point R of the circle. Prove that point R bisects the arc PRQ.

Question 15
The lengths of three consecutive sides of a quadrilateral circumscribing a circle are 4 cm, 5 cm, and 7 cm respectively. Find the length of the fourth side.
[Ans 6 cm]
Hint:
x + y = 4 ….(i) Y + z = 5 …(ii) a + z = 7 ….(iii)
Adding (i), (ii), (iii)
we get: x + 2y + 2z + a = 16 ......(iv)
Eqn.(iv) – 2 X Eqn (ii) : x + a = 6

OR
Sum of opposite sides are equal
AB + CD = BC + DA
4 + 7 = 5 + x
⇒  x  = 11-5 = 6
Question 16
From an external point p, two tangents PA and PB are drawn to the circle with centre O. Prove that OP is the perpendicular bisector of AB

Question 16
From an external point p, two tangents PA and PB are drawn to the circle with centre O. Prove that OP is the perpendicular bisector of AB






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