RMO
RMO or Regional Math Olympiad is the first round of mathematics contest (in India) leading to the prestigious International Mathematics Olympiad. It is held in December (the first Sunday of December). The test is conducted in each of the 19 regions of India. From each region, about 30 students are selected for the next level … Continue reading RMO
In a right triangle ABC, right angled at B, BC = 15 cm, and AB = 8 cm. A circle is inscribed in triangle ABC. What is the radius of the circle?
We can directly use the formula r=Δ/s where r is the radius of in-circle, Δ is the area of the triangle and s is the semi-perimeter. Since its a right-angled triangle, we can use Pythagoras Theorem to find the third side.AC^2 = AB^2 + BC^2AC = 17 cm semi−perimeter = s = (AB+BC+CA)/2 = 20cm Δ = (base∗height)/2 = 60 sq.cm. … Continue reading In a right triangle ABC, right angled at B, BC = 15 cm, and AB = 8 cm. A circle is inscribed in triangle ABC. What is the radius of the circle?
What is the y intercept for the equation y=-10x+14?
Intercept form of a line is given by x/a + y/b = 1 y=−10x+14y ..(transposing −10x to LHS)10x+y=14 ..(dividing both sides by 14)(x/1.4)+(y/14)=1 This is the intercept form of a line.So, the y-intercept point of the line is (0,14); and the length of the y-intercept is 14 units.
How do you prove that SinA+Sin(120+A) +Sin(240+A) =0?
Identities to be used: sin(90+A)=cosAsin(270−A)=−cosAcos(A+B)=cosAcosB−sinAsinBcos(A−B)=cosAcosB+sinAsinB ATQ sinA+sin(120+A)+sin(240+A)=sinA+sin(90+(30+A))+sin(270−(30−A))=sinA+cos(30+A)−cos(30−A)=sinA+cos30.cosA−sin30.sinA−cos30.cosA−sin30.sinA=sinA−2sin30.sinA=sinA−sinA=0 Hence, Proved.