Question : In $\triangle \mathrm{ABC}$, AB = AC, and D is a point on side AC such that BD = BC. If AB = 12.5 cm and BC = 5 cm, then what is the measure of DC?

Option 1: 2 cm

Option 2: 2.5 cm

Option 3: 3 cm

Option 4: 1.8 cm

Question : In $\Delta$ABC, D is the mid-point of BC and G is the centroid. If GD = 5 cm then the length of AD is:

Option 1: 10 cm

Option 2: 12 cm

Option 3: 15 cm

Option 4: 20 cm

Question : The sides AB, BC, and AC of a $\triangle {ABC}$ are 12 cm, 8 cm, and 10 cm respectively. A circle is inscribed in the triangle touching AB, BC, and AC at D, E, and F respectively. The difference between the lengths of AD and CE is:

Option 1: 4 cm

Option 2: 5 cm

Option 3: 3 cm

Option 4: 2 cm

Question : Two chords AB and CD of a circle intersect each other at P internally. If AP = 3.5 cm, PC = 5 cm, and DP = 7 cm, then what is the measure of PB?

Option 1: 8 cm

Option 2: 12 cm

Option 3: 10 cm

Option 4: 10.5 cm

Question : In a circle, chords AB and CD intersect internally at E. If CD = 18 cm, DE = 5 cm, AE = 13 cm, then the length of BE is:

Option 1: 4 cm

Option 2: 7 cm

Option 3: 3 cm

Option 4: 5 cm