Area between four touching circles in a circle | Circle theorems exam questions | Challenging MATHs

Описание: PICK OF THE WEEK Challenging MATHs Problems and Questions
Problem 3 Hard level. General MATHs Challenging questions

GCSE MATHs Circle theorems exam questions | Circles sharing a common point Problem 3 Hard level

This topic is a subtopic for Circle Geometry, so hope you are familiar with Circle properties and theorems.

Make sure, you watched the previous video:

   • GCSE MATHs Circle theorems questions | GCS...  
GCSE MATHs Circle theorems questions | GCSE Higher MATHs 2020 Circle Problem 1 Medium level
   • GCSE MATHs Circle theorems exam questions ...  
GCSE MATHs Circle theorems exam questions | Two circles tangent to each other Challenging MATHs Problem 2 Medium Hard level . Challenging MATHs

where I considered several circle theorems and demonstrate its application to a medium level problem.

Here we will have a walk through a problem of a hard level where four circles are in a larger circle. We will apply several Circle Theorems and the principle of symmetry.


CIRCLE THEOREMS

Tangents from an external point: Tangents from an external point are equal in length.
Radius and a tangent: The tangent to a circle is perpendicular to the radius at the point of contact (common point)

Chords of a circle: The perpendicular from the centre of a circle to a chord bisects the chord.

Angle in a semi-circle: The angle in a semicircle is a right angle.

If a circle can be drawn through four points we say that the points are concyclic and by joining them we can form a convex quadrilateral. That quadrilateral becomes a cyclic quadrilateral.

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