Bissoy.com
Doctors Medicines MCQs Q&A

A circle of radius of 10 cm and another circle whose radius is 20% less than that of first circle, intersect at the points P and Q. If length of PQ is 20% more than the radius of first circle. The distance between the centers of the circle is x cm. What is value of x?

A circle of radius of 10 cm and another circle whose radius is 20% less than that of first circle, intersect at the points P and Q. If length of PQ is 20% more than the radius of first circle. The distance between the centers of the circle is x cm. What is value of x? Correct Answer 13.3

Radius of the first circle OP = 10 cm

Radius of the other circle O’P = 10 × = 8 cm

Length of PQ = 10 × = 12 cm

As we know, PM = PQ/2, PM = 6 cm

[ alt="F2 V.G Deepak 10.08.2019 D1" src="//storage.googleapis.com/tb-img/production/19/10/F2_V.G_Deepak_10.08.2019_D1.png" style="width: 151px; height: 112px;">

In ΔPO’M

By using Pythagoras Theorem

⇒ (O’P)2 = (O’M)2 + (PM)2

⇒ 82 = (O’M)2 + 62

⇒ O’M = √28 cm

In ΔPOM

By using Pythagoras Theorem

⇒ (OP)2 = (OM)2 + (PM)2

⇒ 102 = (OM)2 + 62

⇒ OM = 8 cm

⇒ O’O = OM + O’M = √28 + 8 = 5.3 + 8 = 13.3 cm

Related Questions

“What is the different between height and radius of solid cylinder?” Which of the following option is sufficient alone to find the answer? A) A solid cylinder is made by melting a solid sphere. The radius of cylinder is 3 times the radius of a circle whose area is 154 sq.m. Height of cylinder is equal to the height of cone whose volume is 2772 cubic meters. B) Area of a rectangle whose longer side is ¾ times the radius of a solid cylinder, is 168 sq.m and, Volume of solid cylinder is 2772 cubic meters and its height is 18 m. C) A metallic cone of radius 15m and height 35m is melted into the solid cylinder of radius equal to the radius of a circle whose area is equal to the area of rectangle whose sides are in the ratio 4 : 3 respectively. D) The curved surface area of the solid cylinder is 3 time the surface area of a sphere of radius 7m and height of cylinder is equal to the height of a metallic cone whose curved surface area is 308 sq.m. 
Mohan traveled five cities (A, B, C, D and E) starting from home by a car which has a mileage such that the car can travel 10 km in 1 liter petrol. Distance between city A and B is twice the distance between home to city A. Distance between city B and C is thrice the distance between home to city A. Distance between city C and D is 100. Distance between city D and E is 1.5 times than the distance between B and C. Average distance traveled by Mohan was 41 km between five cities. Find how much petrol was needed by Mohan to travel from city B to D.
Each of the question below consists of a question and three statements number I, II and III given below it. You have to decide whether the data provided in the statement are sufficient to answer the question. If the bus is travelling from Surat to Ahmadabad and a car is travelling from Ahmadabad to Surat, then what is the distance between Surat and Ahmadabad? I. The speed of a car is 40% less than the speed of bus. Bus started at 9 am and car started at 10 am and they meet at 3 pm of the same day. II. After travelling for 1 hour, because of traffic average speed of bus is decreased by 20% and covers distance between Surat to Ahmadabad in 11 hours. Original speed of car is 20% less than original speed of bus and before crossing bus it covered 200 km if starts 1 hour later than bus. After crossing car, bus covers remaining distance in 5 hours. III. Speed of bus is 10 km/hr more than the speed of car and before crossing car ratio of distances covered bus and car in same time was 5 : 4. Time taken by car to cover the distance between Ahmadabad and Surat is 2 hours 15 minutes more than time taken by bus to cover the same distance.
From the given table, what is the percentage of students scoring 40 or more, but less than 70. Scores Less than 20 Less than 30 Less than 40 Less than 50 Less than 60 Less than 70 Less than 80 No. of Students 12 19 22 31 38 46 50
In a quiz competition, Ashok got 72 points. Binod got 9 points more than Ashok but 7 points less than Deepak. Gaurav got 5 points less than Hanif, and 6 points more than Deepak. Who won the quiz competition and how many marks have got?
Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose among the possible answers. Quantity I: A circle whose radius is 56 cm and The Rectangle whose length and breadth are in the ratio 7 ∶ 22 respectively. The area of a circle is equal to the area of a rectangle then calculate the perimeter of the rectangle. Quantity II: A cylinder whose radius is (1/7) of the radius of the circle and the height of the cylinder is twice the radius of the circle and the area of the circle is 154 cm2 then, find the volume of the cylinder.
Amit travels a certain distance with 3 bikes- A, B and C. The speed of bike C is 1 km/hour less than the speed of bike B, the speed of bike B is one less than the bike A. Amit travelled 330 km with bike A. He travelled a distance which is 120 km less than the previous distance of bike B and the distance he travelled on bike C was 60 km more than the distance he travelled at bike B. He took a total time of 81 hours to travel the entire distance on 3 bikes. Find the speed of bike A?
Which of the following statements is/are true? A: If a circle is formed from a wire, which was initially in the shape of a semi-circle, then ratio of radius of circle and that of semi-circle will be 7: 11. B: If in a semi-circle of radius ‘r’, another semi-circle of radius ‘4r/5’ is drawn, then area of the remaining part of larger semi-circle will be ‘3πr2/5’. C: In a circle of radius ‘r’, if ‘O’ is the center of circle and radii OA and OB are at the angle of 45°, then the length of major arc AB will be ‘7πr/8’.
Two equal circles pass through their centers. If radius of every circle is 5 cm. Which of the statements is correct? A. The length of common chord is equal to 5√3 cm B. Distance between the centers of two circle is equal to radius.
Six persons A, B, C, D, E and F were playing a card game. A’s father, mother and uncle were in the group. There were two females. B, the mother of A got more points than her husband. D got more points in the game than E but less than F. Niece of E got the lowest points. Father of A got more points than F but still could not win the game. Who won the game?