Premium Online Home Tutors

3 Tutor System

Starting just at 265/hour

Find the Length of the string of each phone.

Answer :

Let Ankur, Syed and David standing on the point P, Q and R.

Let PQ = QR = PR = X

\(\therefore \) DPQR is an equilateral traingle.

Drawn altitudes PC, QD and RN from vertices to the sides of a traingle and intersect these altitudes at the centre of a circle M.

As PQR is an equilateral, therefore these altitudes bisects their sides.

In \(\triangle{PQC}\),

\({PQ}^2 = {PC}^2 + {QC}^2 \)

(By Pythagoras theorem)

\(\Rightarrow \) \({x}^2 = {PC}^2 + ( \frac{x}{2} )^2 \)

\(\Rightarrow \)\({PC}^2 = {x}^2 - (\frac{x}{2} )^2\)

\(\Rightarrow \) \({PC}^2 = {x}^2 - \frac{x^2}{4} = 3\frac{x^2}{4} \)

(Since, QC = \( \frac{1}{2} \) QR = \(\frac{x}{2} \) )

\(\therefore \) PC = \(\frac{\sqrt{3}x}{2} \)

Now, MC = PC - PM = \(\frac{\sqrt{3}x}{2} \) - 20

(Since, PM = radius)

Now, in \(\triangle{QCM}\),

\({QM}^2 = {QC}^2 + {MC}^2 \)

(By Pythagoras theorem)

\(\Rightarrow \) \( 20^2 = (\frac{x}{2} )^2 + (\frac{\sqrt{3}x}{2} - 20)^2 \)

(Since, QM = radius)

\(\Rightarrow \) \(400 = \frac{x^2}{4} +( \frac{\sqrt{3}x}{2})^2 - 20\sqrt{3}x + 400\)

\(\Rightarrow \) \(0 = {x}^2 - 20\sqrt{3}x\)

\(\Rightarrow \) \({x}^2 = 20\sqrt{3}x\)

\(\therefore \) \(x = 20\sqrt{3}\)

Hence, PQ = QR = PR = \(20\sqrt{3}\)m.

- Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.
- If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.
- If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.
- If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D. prove that AB = CD (see figure).
- Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, and Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is 6 m each, what is the distance between Reshma and Mandip?

- NCERT solutions for class 9 maths chapter 1 Number Systems
- NCERT solutions for class 9 maths chapter 2 Polynomials
- NCERT solutions for class 9 maths chapter 3 Coordinate geometry
- NCERT solutions for class 9 maths chapter 4 Linear equations in two variables
- NCERT solutions for class 9 maths chapter 5 Introduction to Euclidean Geometry
- NCERT solutions for class 9 maths chapter 6 Lines and Angles
- NCERT solutions for class 9 maths chapter 7 Triangles
- NCERT solutions for class 9 maths chapter 8 Quadrilaterals
- NCERT solutions for class 9 maths chapter 9 Areas of parallelograms and triangles
- NCERT solutions for class 9 maths chapter 10 Circles
- NCERT solutions for class 9 maths chapter 11 Constructions
- NCERT solutions for class 9 maths chapter 12 Heron's Formula
- NCERT solutions for class 9 maths chapter 13 Surface areas and volumes
- NCERT solutions for class 9 maths chapter 14 Statistics
- NCERT solutions for class 9 maths chapter 15 Probability

- NCERT solutions for class 9 science chapter 1 Matter in our Surroundings
- NCERT solutions for class 9 science chapter 2 Is Matter Around Us Pure
- NCERT solutions for class 9 science chapter 3 Atoms and Molecules
- NCERT solutions for class 9 science chapter 4 Structure of the Atom
- NCERT solutions for class 9 science chapter 5 The Fundamental Unit of Life
- NCERT solutions for class 9 science chapter 6 Tissues and Fundamental unit of life
- NCERT solutions for class 9 science chapter 7 Diversity in Living Organisms
- NCERT solutions for class 9 science chapter 8 Motion
- NCERT solutions for class 9 science chapter 9 Force and Laws of Motion
- NCERT solutions for class 9 science chapter 10 Gravitation
- NCERT solutions for class 9 science chapter 11 Work and Energy
- NCERT solutions for class 9 science chapter 12 sound
- NCERT solutions for class 9 science chapter 13 Why do We Fall Ill
- NCERT solutions for class 9 science chapter 14 Natural Resources
- NCERT solutions for class 9 science chapter 15 Improvement in Food Resources