41. In the given figure MNOP is a parallelogram. PM is extended to Z. OZ intersects MN and PN at Y and X respectively. If OX = 27 cm and XY = 18 cm, then what is the length (in cm) of YZ?
42. A, B, C are three points so that AB = 4 cm, BC = 6 cm and AC = 10 cm. The number of circles passing through the points A, B, C is
43. Let two chords AB and AC of the larger circle touch the smaller circle having same centre at X and Y. Then XY = ?
44. In a circle with centre O, a diameter AB is produced to a point P lying outside the circle and PT is a tangent to the circle at the point C on it. If ∠BFT = 36°, then is the measure of ∠BCP?
45. ABC is an equilateral triangle with side 12 cm and AD is the median. Find the length of GD is G is the centroid of ΔABC.
46. In the given figure, ∠DBC = 65°, ∠BAC = 35° and AB = BC, then the measure of ∠ECD is equal to:
47. In ΔABC, AB = AC and D is a point on BC. If BD = 5 cm, AB = 12 cm and AD = 8 cm, then the length of CD is:
48. In ΔPQR, the side QR is extended to S such that RS = PR. If ∠QPS = 110° and ∠PRQ = 70°, then the value of ∠PQR is:
49. Chords AC and BD of a circle with centre O intersect at right angles at E. If ∠OAB = 25°, then the value of ∠EBC is
50. PQRS is a cyclic quadrilateral. If ∠P is 4 times ∠R, and ∠S is 3 times ∠Q, then the average of ∠Q and ∠R is:
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