M CUBE: Math-e-Matics by Maheshwari PRMO

Let S be a circle with centre be O. A chord AB, not the diameter, divides S into two regions R1 and R2 such that O belongs to R2. Let S1 be a circle with centre in R1, touching AB at X and S internally. Let S2 be a circle with centre in R2, touching AB at Y, the circle S internally, and passing through the centre of S. The point X lies on the diameter passing through the centre of S2 and angle YXO = 30 degrees. If the radius of S2 is 100 units, find the length of the radius of S1?

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M CUBE: Math-e-Matics by Maheshwari Basic Mathematics

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?