mc8sz_theorem

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 &#x22A5 AC Proof: 1.  OB < OC || Since each point of the tangent other than ... Read more

Theorem: The angle in a semicircle is a right angle Given : A circle with centre 0 with  &#x2220A0B at centre and  &#x2220ACB at the circumference of the circle . RT.P. : the angle in a semicircle is a right angle. ie : &#x2220 ACB= 90o Statements: 1   &#x2220AOB = 2&#x2220ACB  ||  angle at the … Read more

Theorem : Opposite Angles of a Cyclic Quadrilateral are Supplementary. Solution : Given: ABCD is a cyclic quadrilateral.R.T.P.(Require To Prove) 1. &#x2220BAD + &#x2220BCD = 1800      2. &#x2220ABC + &#x2220ADC = 1800 Construction : Join OB and OD Proof: 1. &#x2220 BOD = 2 ∠BAD || Angle at the centre of a circle is … Read more

Theorem : A circle  with centre O in which AB subtends  &#x2220AOB at centre and angle &#x2220ACB at any point  on the remaining part of the circle. R.T.P. – &#x2220AOB =  2 x &#x2220ACB Solution : Construction: Join CO and produce CO to point D . 1. In ∆AOC, OC = OA || Radii of … Read more