Understanding Elementary Shapes (IMO- Mathematics Olympiad Class 6): Questions 53 - 54 of 82

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Question number: 53

» Understanding Elementary Shapes

MCQ▾

Question

In figure, the side BC of ABC is produced to E, where ACE=1200 . If CD bisects ACB and BAC=600 , find DCB and DBC respectively.

Triangle poly1 Triangle poly1: Polygon A, B, CArc d Arc d: Semicircle through F and GArc e Arc e: Semicircle through J and KSegment c Segment c: Segment [A, B] of Triangle poly1Segment a Segment a: Segment [B, C] of Triangle poly1Segment b Segment b: Segment [C, A] of Triangle poly1Segment f Segment f: Segment [C, D] Segment g Segment g: Segment [C, E] Point A A = (5, 5) Point A A = (5, 5) Point A A = (5, 5) Point B B = (3.26, 2) Point B B = (3.26, 2) Point B B = (3.26, 2) Point C C = (7.44, 1.98) Point C C = (7.44, 1.98) Point C C = (7.44, 1.98) Point D Point D: Point on cPoint D Point D: Point on cPoint D Point D: Point on cPoint E E = (12, 2) Point E E = (12, 2) Point E E = (12, 2) 120? text1 = “120? “60? text1_1 = “60? “

Image of a Triangle ABC Having a Bisector CD and One Given Angle

Showing an image of a triangle ABC having a bisector CD then find angle DCB and DBC

Choices

Choice (4) Response

a.

600,900

b.

600,700

c.

300,600

d.

300,500

Question number: 54

» Understanding Elementary Shapes

MCQ▾

Question

Find the value of x.

Line f Line f: Line through O, BLine f Line f: Line through O, BLine i Line i: Line through O, DLine i Line i: Line through O, DRay g Ray g: Ray through O, CRay h Ray h: Ray through O, ARay j Ray j: Ray through O, EPoint O O = (5.68, 3.02) Point O O = (5.68, 3.02) Point O O = (5.68, 3.02) Point B B = (8.66, 5.42) Point B B = (8.66, 5.42) Point B B = (8.66, 5.42) Point A A = (10, 3) Point A A = (10, 3) Point A A = (10, 3) Point D D = (2.96, 0.82) Point D D = (2.96, 0.82) Point D D = (2.96, 0.82) Point E E = (9.5, 1.66) Point E E = (9.5, 1.66) Point E E = (9.5, 1.66) Point C C = (5.68, 5.88) Point C C = (5.68, 5.88) Point C C = (5.68, 5.88) (3x 10)? text1 = ” (3x 10)? “ (x-30)? text2 = ” (x-30)? “ (2x)? text3 = ” (2x)? “ (2x-40)? text4 = ” (2x-40)? “ (2x-20)? text5 = ” (2x-20)? “

Image Made by Some Lines That Make Some Angles

Find the value of x by using given angles

Choices

Choice (4) Response

a.

550

b.

600

c.

400

d.

440

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