In a circle with centre O, AB is the diameter. P and Q are two points on the circle on the same side of the diameter AB. AQ and BP intersect at C. If ∠POQ = 54°, then the measure of ∠PCA is:

The two vowels touch each other internally. Their radii are 2 cm and 3 cm. What will be the length of the largest chord of the bigger circle outside the inner circle?

Let ΔABC ∼ Δ PQR and ar(∆ABC)/ar(∆PQR) =4/25. If AB = 12 cm, BC = 8 cm and AC = 9 cm, then QR is equal to:

P is a point outside a circle and is 26 cm away from its centre. A secant PAB drawn form P intersects the circle at points A and B such that PB=32 cm and PA=18cm. The radius of the circle (in cm) is:

If △ABC is right angled at B, AB = 12 cm and ∠CAB = 60°, determine the length of BC.

If the circumradius of an equilateral triangle be 10 cm, then the measure of its in-radius is

If the ratio of the heights of two identical triangles is 4: 9, find the ratio of the areas of the two triangles.

The diameter of the circle with center O is AB. PQ is the chord that does not intersect AB. Join AP and BQ. If ∠BAP = ∠ABQ,  then what will be ABQP?