The perpendicular from the center of a circle to a chord bisects the chord. Given: A circle with center O, AB is chord of a circle and OC perpendicular from the center O to the chord AB. i.e. OC ⊥ AB therefore ∠OCA and ∠OCB, Both angles are 900. To prove: AC = CB Construction: join OA and OB. Proof: In △OCA and △ OCB ∠OCA = ∠OCB […]
Read More →Definition, Properties, Examples – Cyclic Quadrilaterals What is a Cyclic Quadrilateral A cyclic quadrilateral is a four sided polygon that is inscribed in a circle. The vertices are said concyclic. The center of the circle is called circumcenter and radius of the circle is called circumradius. Definition: A Cyclic Quadrilateral is a quadrilateral, whose all four vertices […]
Read More →The Pythagoras Theorem A long time over 2000 years ago, a Greek mathematician named Pythagoras discovered an amazing and interesting property about Right triangles, The square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides. This property now called Pythagoras […]
Read More →What is an Acute Triangle: Definition, Formula and Properties In geometry, a triangle is a polygon with three sides, three vertices and three interior angles. In other words a triangle is a closed two dimensional plane figure with three sides and three angles. Triangles are classified on the basis of their sides and angles. There […]
Read More →Hypotenuse of a triangle In geometry, the longest side of a right-angled triangle, the side opposite the right angle is known as hypotenuse. Pythagoras theorem applies to right triangles and states that, The square on the hypotenuse is equal to the sum of the squares on the other two sides. (hypotenuse)2 = (Base)2+(Perpendicular)2 […]
Read More →Solutions of Trigonometric Ratios (1) If sin A = 4/5, find the other trigonometric ratios of the angle A. Solution: Let us draw a right △ ABC in which ∠B = 900 We know that, sin A = 4/5 = BC/AC Therefore, if BC =4k, then AC = 5k, where k is a positive number. Now, using […]
Read More →Trigonometric ratios in right triangles In a triangle, if any one angle is a right angle ( that is a 90 degree angle) then the triangle is called right triangle. A triangle has three sides, the longest side of the triangle is opposite of right angle called Hypotenuse, and the other two sides including the right […]
Read More →What is Theorem in Mathematics In mathematics a theorem is a statement, that has been proved to be true on basis of facts that were already known and used in previously established statements. The process of showing a theorem to be (true) correct is called proof. proofs are an important part of mathematics. […]
Read More →Circumscribes and Inscribed Circles Circumscribed Circle The circumscribed circle is one and only one circle that always passes through all three vertices (corners) of the triangle. The center of the circumscribed circle is a point where all the three perpendicular bisectors of the triangles sides are meet. The center of the circumscribed circle is known ascircumcenter of the triangle. […]
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