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Resources tagged with Radius (radii) & diameters similar to Orthogonal Circle:

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Broad Topics > 2D Geometry, Shape and Space > Radius (radii) & diameters

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Just Touching

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Three semi-circles have a common diameter, each touches the other two and two lie inside the biggest one. What is the radius of the circle that touches all three semi-circles?

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Circles in Circles

Stage: 5 Challenge Level: Challenge Level:1

This pattern of six circles contains three unit circles. Work out the radii of the other three circles and the relationship between them.

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Some(?) of the Parts

Stage: 4 Challenge Level: Challenge Level:1

A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle

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Medallions

Stage: 4 Challenge Level: Challenge Level:1

I keep three circular medallions in a rectangular box in which they just fit with each one touching the other two. The smallest one has radius 4 cm and touches one side of the box, the middle sized. . . .

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Escriptions

Stage: 5 Challenge Level: Challenge Level:1

For any right-angled triangle find the radii of the three escribed circles touching the sides of the triangle externally.

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Circle-in

Stage: 4 Challenge Level: Challenge Level:1

A circle is inscribed in a triangle which has side lengths of 8, 15 and 17 cm. What is the radius of the circle?

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Incircles

Stage: 5 Challenge Level: Challenge Level:1

The incircles of 3, 4, 5 and of 5, 12, 13 right angled triangles have radii 1 and 2 units respectively. What about triangles with an inradius of 3, 4 or 5 or ...?

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Salinon

Stage: 4 Challenge Level: Challenge Level:1

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

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Incircles Explained

Stage: 5

This article is about triangles in which the lengths of the sides and the radii of the inscribed circles are all whole numbers.

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The Eyeball Theorem

Stage: 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Two tangents are drawn to the other circle from the centres of a pair of circles. What can you say about the chords cut off by these tangents. Be patient - this problem may be slow to load.

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Circle Box

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

It is obvious that we can fit four circles of diameter 1 unit in a square of side 2 without overlapping. What is the smallest square into which we can fit 3 circles of diameter 1 unit?

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Just Rolling Round

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

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Perfect Eclipse

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Use trigonometry to determine whether solar eclipses on earth can be perfect.

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Far Horizon

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

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Arrh!

Stage: 4 Challenge Level: Challenge Level:1

Triangle ABC is equilateral. D, the midpoint of BC, is the centre of the semi-circle whose radius is R which touches AB and AC, as well as a smaller circle with radius r which also touches AB and AC. . . .

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Flower

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Six circles around a central circle make a flower. Watch the flower as you change the radii in this circle packing. Prove that with the given ratios of the radii the petals touch and fit perfectly.

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Sangaku

Stage: 5 Challenge Level: Challenge Level:1

The square ABCD is split into three triangles by the lines BP and CP. Find the radii of the three inscribed circles to these triangles as P moves on AD.