Скачать или смотреть GCSE MATHs Circle theorems Edexcel exam questions | Inscribed angle Central Angle Area of triangle

Problem 4 Medium level . GCSE Higher MATHS

GCSE Higher MATHs 2020 Circles
GCSE MATHs Circle theorems exam questions | Inscribed angle, Central Angle, Area of triangle through two sides and sin of the angle between them

This is new series dedicated to Circle Theorems Questions and Problems GCSE Higher Maths and iGCSE Extended. This topic is a subtopic for Circle Geometry, so hope you are familiar with Circle properties and theorems

Make sure, you watched the previous series of videos dedicated to Basics:
   • GCSE MATHs Circle theorems questions | GCS...  
GCSE MATHs Circle theorems questions | GCSE Higher MATHs 2020 Circle Problem 1 Medium level

and

   • GCSE MATHs Circle theorems exam questions ...  

GCSE MATHs Circle theorems exam questions | Two circles tangent to each other Challenging MATHs

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

Here we will have a walk through two problems of a medium level where circles will have tangent lines. We will apply several Circle Theorems.

During discussion in the 1st problem I will share three ways of finding the angle. This approach you might use as a shortcut for other similar problems


Quick Reminder:

CIRCLE THEOREMS

A circle is the set of all points (LOCI) which are equidistant from a fixed point called the centre

The circumference is the distance or the length around the entire circle boundary.

An arc of a circle is any continuous part of the circle. A chord of a circle is a line segment joining any two points on the circle. A radius of a circle is any line segment joining its centre to any point on the circle. A diameter of a circle is any chord passing through its centre.

A semicircle is a half of a circle.

A tangent to a circle is any line which touches the circle in exactly one point.

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.

Optimization:
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