IMO Level 1 Mathematics Olympiad (SOF) Class 10: Questions 810  812 of 968
Access detailed explanations (illustrated with images and videos) to 968 questions. Access all new questions we will add tracking exampattern and syllabus changes. Subscription can be renewed yearly absolutely FREE! View Sample Explanation or View Features.
Rs. 450.00 or
How to register?
Question number: 810
» Triangle, Circle & Constructions
Question
Let PQR be a right triangle in which . QS is the perpendicular from Q on PR. The circle through Q, R, and S is drawn from P to this circle. Given below are the steps of constructions of a pair of tangents. Find out the wrong step.

Step I: Draw and perpendicular QS from Q on PR.

Step II: Draw a circle with QR as a diameter. This circle will pass through S.

Step III: Let O be the midpoint of QR. Join PO.

Step IV: Draw a circle with PO as diameter. This circle cuts the circle drawn in step II Q at T. join PO, PT and PQ are desired tangents drawn from P to the circle passing through Q, R and S.
Choices
Choice (4)  Response  

a.  Only 1 

b.  Only 2 

c.  Only 3 

d.  Only 4 

Question number: 811
Question
A right triangle, whose sides are and 4 (other than hypotenuse) is made to revolve about its hypotenuse. The volume of the double cone so formed is ________
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 812
» Triangle, Circle & Constructions
Question
Give below are the steps of construction of (without using the center of the circle radius) two tangents to the circle from point Q.

Step I: Draw a line segment Take a point Q outside the circle and draw a secant QRO, intersecting the circle at R and O.

Step II: Produce to to P such that draw a semicircle with as diameter.

Step III: Draw intersecting the semicircle at S. with Q as center and PQ as radius draw arcs to intersect the given circle at A and A’.

Step IV: Join QA and QA’. Then, QA and QA’ are the required tangents.
Choices
Choice (4)  Response  

a.  2 

b.  3 

c.  1 

d.  4 
