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#### Resources tagged with Perpendicular lines similar to Square World:

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### There are 14 results

Broad Topics > 2D Geometry, Shape and Space > Perpendicular lines

### Square World

##### Stage: 5 Challenge Level:

P is a point inside a square ABCD such that PA= 1, PB = 2 and PC = 3. How big is angle APB ?

### Orthogonal Circle

##### Stage: 5 Challenge Level:

Given any three non intersecting circles in the plane find another circle or straight line which cuts all three circles orthogonally.

### At Right Angles

##### Stage: 4 Challenge Level:

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

### Three Way Split

##### Stage: 4 Challenge Level:

Take any point P inside an equilateral triangle. Draw PA, PB and PC from P perpendicular to the sides of the triangle where A, B and C are points on the sides. Prove that PA + PB + PC is a constant.

### Tricircle

##### Stage: 4 Challenge Level:

The centre of the larger circle is at the midpoint of one side of an equilateral triangle and the circle touches the other two sides of the triangle. A smaller circle touches the larger circle and. . . .

### Angle Trisection

##### Stage: 4 Challenge Level:

It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.

### The Dodecahedron Explained

##### Stage: 5

What is the shortest distance through the middle of a dodecahedron between the centres of two opposite faces?

### Shrink

##### Stage: 4 Challenge Level:

X is a moveable point on the hypotenuse, and P and Q are the feet of the perpendiculars from X to the sides of a right angled triangle. What position of X makes the length of PQ a minimum?

##### Stage: 4 Challenge Level:

Find the area of the shaded region created by the two overlapping triangles in terms of a and b?

### Similarly So

##### Stage: 4 Challenge Level:

ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.

##### Stage: 5 Challenge Level:

A quadrilateral changes shape with the edge lengths constant. Show the scalar product of the diagonals is constant. If the diagonals are perpendicular in one position are they always perpendicular?

### Perpendicular Lines

##### Stage: 4 Challenge Level:

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?

### Walls

##### Stage: 5 Challenge Level:

Plane 1 contains points A, B and C and plane 2 contains points A and B. Find all the points on plane 2 such that the two planes are perpendicular.