# Category: mc8sz_theorem

## Theorem: Tangent and Radius of a Circle | are Perpendicular to Each Other.

Theorem :Tangent and radius of a circle are perpendicular to each other. Solution : Given: A circle with centre O. AB is the tangent to the circle at point B and OB is the radius of the circle.R.T.P. OB ⊥ AC Proof: 1. OB < OC || Since each point of the tangent other than…

## Theorem : The Angle in a Semi-Circle is a Right Angle

Theorem: The angle in a semicircle is a right angle Given : A circle with centre 0 with � at centre and � at the circumference of the circle . RT.P. : the angle in a semicircle is a right angle. ie : ∠ ACB= 90o Statements: 1 𢈊OB = 2� || angle at the…

## Theorem : Opposite Angles of a Cyclic Quadrilateral are Supplementary | Class 8

Theorem : Opposite Angles of a Cyclic Quadrilateral are Supplementary. Solution : Given: ABCD is a cyclic quadrilateral.R.T.P.(Require To Prove) 1. � + � = 1800 2. � + � = 1800 Construction : Join OB and OD Proof: 1. ∠ BOD = 2 ∠BAD || Angle at the centre of a circle is…

## Theorem | the angle subtended by an arc of a circle | at the centre is double the angle subtended by it at | any point on the remaining part of the circle

Theorem : A circle with centre O in which AB subtends 𢈊OB at centre and angle � at any point on the remaining part of the circle. R.T.P. – 𢈊OB = 2 x � Solution : Construction: Join CO and produce CO to point D . 1. In ∆AOC, OC = OA || Radii of…