41. Let ΔABC and ΔABD be on the same base AB and between the same parallels AB and CD. Then the relation between areas of triangles ABC and ABD will be
42. In a triangle ABC, D is a point on BC such that $$\frac{{{\text{AB}}}}{{{\text{AC}}}} = \frac{{{\text{BD}}}}{{{\text{DC}}}}.$$ If ∠B = 68° and ∠C = 52°, then measure of ∠BAD is equal to:
43. Two chords AB and CD of a circle with centre O intersect at P. If ∠APC = 40°. Then the value of ∠AOC + ∠BOD is
44. If in ΔPQR, ∠P = 120°, PS ⊥ QR at S and PQ + QS = SR, then the measure of ∠Q is:
45. The radius of two circles is 3 cm and 4 cm. The distance between the centres of the circles is 10 cm. What is the ratio of the length of direct common tangent to the length of the transverse common tangent?
46. In the given figure, diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. If CD = 7.8 cm, PD = 5 cm, PB = 4 cm, find AB.
47. In the following figure, if angles ∠ABC = 95°, ∠FED = 115° (not to scale). Then the angle ∠APC is equal to:
48. The orthocentre of a triangle is the point where
49. ΔPQR is an isosceles triangle and PQ = PR = 2a unit, QR = a unit. Draw PX ⊥ QR, and find the length of PX.
50. The sides BA and DE of a regular pentagon are produced to meet at F. What is the measure of ∠EFA?
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