IMO Level 1- Mathematics Olympiad (SOF) Class 10: Questions 747 - 749 of 968

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Question number: 747

» Triangle, Circle & Constructions

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MCQ▾

Question

In the figure, and intersect at M. then________.

Circle c Circle c: Circle through B_1 with center P Circle d Circle d: Circle through D_1 with center Q Segment f Segment f: Segment [P, Q] Segment g Segment g: Segment [R, S] Point P P = (-1.58,2.96) Point P P = (-1.58,2.96) Point P P = (-1.58,2.96) Point Q Q = (0.68,2.96) Point Q Q = (0.68,2.96) Point Q Q = (0.68,2.96) Point R Point R: Intersection point of c, d Point R Point R: Intersection point of c, d Point R Point R: Intersection point of c, d Point S Point S: Intersection point of c, d Point S Point S: Intersection point of c, d Point S Point S: Intersection point of c, d Point M Point M: Intersection point of f, g Point M Point M: Intersection point of f, g Point M Point M: Intersection point of f, g

Two Circles Intersect Each Other.

Two circles PQ and RS intersect at M

Choices

Choice (4) Response

a.

b.

c.

d.

Both a. and c. are correct

Question number: 748

» Area, Surface Area & Volume

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MCQ▾

Question

If the radii of the circular ends of a conical bucket are and and the height is the capacity of the bucket is________.

Choices

Choice (4) Response

a.

b.

c.

d.

Question number: 749

» 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 A.

  1. Step I: Draw a line segment Take a point A outside the circle and draw a secant ACD, intersecting the circle at C and D.

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

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

  4. Step IV: Join AS and AS’. Then, AS and AS’ are the required tangents.

Choices

Choice (4) Response

a.

3

b.

2

c.

4

d.

1