DE ∥ BC of ΔABC where D and E are two points on AB and AC, respectively. If AD = 5 cm, DB = 6 cm, and AE = 7.5 cm, calculate the length of AC.

If the lengths of three sides of two triangles are in proportion, then which type of triangle is this?

Perimeters of two similar triangles are 27 cm and 16 cm. If the length of a side of the first triangle is 9 cm, then find the length of the corresponding side of the second triangle

In trapezium ABCD, BC ∥ AD and AD = 4 cm. Diagonals AC and BD meet at O such that AO/OC = DO/OB = 1/2. Find the length of BC.

In ΔABC, L and M are two points on the sides AC and BC respectively such that LM || AB and AL are (x - 2) units, AC = 2x + 3 units, BM = (x – 3) units and BC = 2x units. Determine the value of x.

State True/False: “The equal chords of a circle are at equal distances from the centre of the circle.”

Write a difference between the geometric angle and trigonometrical angle.

Find the value of angle in degree made by the tangent of a circle with the radius of that circle at the point of contact

Mode = 2 × Median – 3 × Mean.

If x be the volume, y be the area of the base and z be the height of a cone then the value of x / yz is 3.

ABCD is a cyclic quadrilateral. If ∠ADB = x° and ∠ABD = y° then ∠BCD is (x + y)°.

If the sum of the square of the roots of the equation 6x² + x + k = 0 is , then the value of k is 12.