In The Given Figure Triangle Abc Is An Equilateral Triangle Inscribed

1 In The Given Figure An Equilateral Triangle Abc Is Inscribed I Calculate: (i) angle abc (ii) angle bec. in the given figure, abc is a triangle in which ∠bac = 30°. show that bc is equal to the radius of the circumcircle of the triangle abc, whose centre is o. the given figure shows a circle with centre o such that chord rs is parallel to chord qt, angle prt = 20° and angle poq = 100°. calculate: (i. In the given figure, a circle is inscribed in an equilateral triangle abc of side 12 cm. find the radius of the inscribed circle and the area of the shaded region. [use √ 3 = 1.73 a n d π = 3.14 ].

An Equilateral Triangle Abc Is Inscribed In A Circle Of Radius 12 Cm In the first two cases, draw a perpendicular line segment from o to ¯ ab at the point d. figure 2.5.2 circumscribed circle for abc. the radii ¯ oa and ¯ ob have the same length r, so aob is an isosceles triangle. thus, from elementary geometry we know that ¯ od bisects both the angle ∠aob and the side ¯ ab. A circle is inscribed in the triangle if the triangle's three sides are all tangents to a circle. in this situation, the circle is called an inscribed circle, and its center is called the inner center, or incenter. since the triangle's three sides are all tangents to the inscribed circle, the distances from the circle's center to the three sides are all equal to the circle&#x27. Advanced properties. firstly, it is worth noting that the circumradius is exactly twice the inradius, which is important as r \geq 2r r ≥ 2r according to euler's inequality. the equilateral triangle provides the equality case, as it does in more advanced cases such as the erdos mordell inequality. A circle is inscribed in an equilateral triangle abc of side 12 cm. find the radius of inscribed circle and the area of the shaded region. [use π = 3.14 a n d √ 3 = 1.73 ] view solution.