![]() Solution: Area of a triangle = (1/2)base × height extended BC, drawing a line from point A and perpendicular to the extended BC line, these two lines intesect at point D AD is the height of the obtuse triangle when base is BC since AD is perpendicular to CD, so triangle ACD is a right triangle since BCD is a straight line so the angle ACB + angle ACD = 180 o angle ACD = 180 o - angle ACB = 180 o - 120 o = 60 o since ACD is a right triangle so sin(angle ACD) = opposite side/hypotenuse that is, sin(angle ACD) = AD/AC so AD = AC sin(angle ACD) = (7 Sqrt (3))(sin60 o) = (7 Sqrt (3))(Sqrt (3))/2 = 7 × 3 ÷ 2 = 21/2 let A be the area of triangle ABC A = (1/2) base × height = (1/2) BC × AD = (1/2) × 6 × 21/2 = 6 × 21 ÷ 4 = 31.5 so the area of the triangle ABC is 31.5 square feet. Hence, \(\therefore\) Figure C represents an orthocenter.Example of finding the area of an obtuse triangle Question: ABC is a triangle, BC = 6 feet and AC = 7 Sqrt (3) feet. Therefore, the orthocenter is a concurrent point of altitudes. The point where the three altitudes of a triangle meet are known as the orthocenter. Ruth needs to identify the figure which accurately represents the formation of an orthocenter. Let us see some solved examples to understand the concept better. Observe the different congruency points of a triangle with the following simulation: The point where three altitudes of the triangle meet is known as the orthocenter.įor an obtuse-angled triangle, the orthocenter lies outside the triangle. It always divides each median into segments in the ratio of 2:1. In Physics, we use the term "center of mass" and it lies at the centroid of the triangle.Ĭentroid always lies within the triangle. The point where three medians of the triangle meet is known as the centroid. The circle that is drawn taking the incenter as the center, is known as the incircle. The incenter always lies within the triangle. ![]() In other words, the point where three angle bisectors of the angles of the triangle meet are known as the incenter. The incenter is the point of concurrency of the angle bisectors of all the interior angles of the triangle. If we draw a circle taking a circumcenter as the center and touching the vertices of the triangle, we get a circle known as a circumcircle. The circumcenter is the point of concurrency of the perpendicular bisectors of all the sides of a triangle.įor an obtuse-angled triangle, the circumcenter lies outside the triangle.įor a right-angled triangle, the circumcenter lies at the hypotenuse. The different points of concurrency in the triangle are: These concurrent points are referred to as different centers according to the lines meeting at that point. These are the perpendicular lines drawn to the opposite side from the vertices of the triangle.Īs four different types of line segments can be drawn to a triangle, similarly we have four different points of concurrency in a triangle. ![]() These line segments connect any vertex of the triangle to the mid-point of the opposite side. These lines bisect the angles of the triangle. These are the perpendicular lines drawn to the sides of the triangle. Please refer to the following table for the above statement: Name of the line segment Four different types of line segments can be drawn for a triangle.
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