21. In equilateral ΔABC, D and E are points on the side AB and AC, respectively, such that AD = CE. BE and CD intersect at F. The measure (in degrees) of ∠CFB is :
22. In ΔABC, D is a point on BC. If $$\frac{{{\text{AB}}}}{{{\text{AC}}}} = \frac{{{\text{BD}}}}{{{\text{DC}}}},$$ ∠B = 75° and ∠C = 45°, then ∠BAD is equal to :
23. In a circle with centre O, chords PR and QS meet at the point T, when produced, and PQ is a diameter. If ∠ROS = 42°, then the measure of ∠PTQ is:
24. There are 8 equidistant points A, B, C, D, E, F, G and H (in same order) on a circle. What is the value of ∠FDH (in degrees)?
25. If in any triangle, the angles are in the ratio of 1 : 2 : 1, then what will be the ratio of its sides?
26. An isosceles ΔMNP is inscribed in a circle. If MN = MP = 16√5 cm, and NP = 32 cm, what is the radius (in cm) of the circle?
27. In ΔABC, AD is a median and P is a point on AC such that AP : PD = 3 : 4. Then ar (ΔAPB) : ar (ΔABC) is equal to:
28. ΔABC a right angled triangle has ∠B = 90° and AC is hypotenuse. D is its circumcenter and AB = 3 cms, BC = 4 cms. The value of BD is
29. In a circle with centre O, ACBO is a parallelogram where C is a point on the minor arc AB. What is the measure of ∠AOB?
30. Two chords AB and CD of a circle with centre O, intersect each other at P. If ∠AOD = 100° and ∠BOC = 70°, then the value of ∠APC is
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