IMO Level 1- Mathematics Olympiad (SOF) Class 10: Questions 810 - 812 of 968

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Question number: 810

» Triangle, Circle & Constructions

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MCQ▾

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.

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

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

  3. Step III: Let O be the mid-point of QR. Join PO.

  4. 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

» Area, Surface Area & Volume

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MCQ▾

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

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MCQ▾

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.

  1. 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.

  2. Step II: Produce to to P such that draw a semi-circle with as diameter.

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

  4. 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