IMO Level 1- Mathematics Olympiad (SOF) Class 7: Questions 631 - 631 of 1022

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Question number: 631

» Triangle and Its Properties

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Question

In the figure (not drawn to scale), EFA is a right-angled triangle with and FGB is an equilateral triangle, find .

Triangle poly1Triangle poly1: Polygon A, B, CQuadrilateral poly2Quadrilateral poly2: Polygon B, E, F, CArc kArc k: Semicircle through D and HArc pArc p: Semicircle through I and JArc qArc q: Semicircle through K and LSegment cSegment c: Segment [A, B] of Triangle poly1Segment aSegment a: Segment [B, C] of Triangle poly1Segment bSegment b: Segment [C, A] of Triangle poly1Segment b_1Segment b_1: Segment [B, E] of Quadrilateral poly2Segment dSegment d: Segment [E, F] of Quadrilateral poly2Segment eSegment e: Segment [F, C] of Quadrilateral poly2Segment c_1Segment c_1: Segment [C, B] of Quadrilateral poly2Segment fSegment f: Segment [B, F] Segment gSegment g: Segment [C, G] Segment hSegment h: Segment [G, F] Point AA = (4.5,4.82) Point AA = (4.5,4.82) Point AA = (4.5,4.82) Point BB = (3.18,3.38) Point BB = (3.18,3.38) Point BB = (3.18,3.38) Point CC = (4.48,3.38) Point CC = (4.48,3.38) Point CC = (4.48,3.38) Point EE = (1.42,1.52) Point EE = (1.42,1.52) Point EE = (1.42,1.52) Point FF = (4.42,1.52) Point FF = (4.42,1.52) Point FF = (4.42,1.52) Point GG = (5.7,3.38) Point GG = (5.7,3.38) Point GG = (5.7,3.38) ytext1 = “y”xtext1_1 = “x”88â°text1_2 = “88â°”

Image of Triangles EFA and FGB

Choices

Choice (4)Response

a.

92

b.

82

c.

27

d.

97

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