41. In the figure, chords AB and CD of a circle intersect externally at P. If AB = 4 cm, CD = 11 cm and PD = 15 cm, then the length of PB is:
42. In the given figure, if AC, DE are parallel and ∠CAB = 38°, then the value of ∠ABC + 5∠CBD is:
43. A, B and C are three points on the circle. If AB = AC = 7√2 cm and ∠BAC = 90° men the radius is equal to:
44. In the given figure, PQ is a diameter of the semicircle PABQ and O is its center. ∠AOB = 64°. BP cuts AQ at X. What is the value (in degrees) of ∠AXP?
45. In the given figure, AQ = 4√2 cm, QC = 6√2 cm and AB = 20 cm. If PQ is parallel to BC, then what is the value (in cm) of PB?
46. Let ABC be an equilateral triangle and AD perpendicular to BC. Then AB2 + BC2 + CA2 =?
47. In ΔABC, ∠A = 90°, AD is the bisector of ∠A meeting BC at D, and DE ⊥ AC at E. If AB = 10 cm and AC = 15 cm, then the length of DE, in cm, is:
48. In the given figure, AB = DB and AC = DC. If ∠ABD = 58° and ∠DBC = (2x - 4)°, ∠ACB = (y + 15)° and ∠DCB = 63° then the value of 2x + 5y is:
49. ΔABC and ΔDBC are on the same base BC but on opposite sides of it. AD and BC intersect each other at O. If AO = a cm, DO = b cm and the area of ΔABC = x cm2, then what is the area (in cm2) of ΔDBC?
50. Triangle ABC is similar to triangle PQR and AB : PQ= 2 : 3. AD is median to the side BC in triangle ABC and PS is the median to side QR in triangle PQR. What is the value of $${\left( {\frac{{{\text{BD}}}}{{{\text{QS}}}}} \right)^2}?$$
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