21. PQR is an isosceles triangle such that PQ = QR = 10 cm and ΔPQR = 90°. What is the length of the perpendicular drawn from Q on PR?
22. ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 118°. What is the measure of ∠BAC?
23. In quadrilateral ABCD, the bisectors of ∠A and ∠B meet at O and ∠AOB = 64°. ∠C + ∠D is equal to:
24. If the parallel sides of a trapezium are 8 cm and 4 cm, M and N are the mid points of the diagonals of the trapezium, then length of MN is.
25. DE is a tangent to the circumcircle of ΔABC at the vertex A such that DE || BC. If AB = 17 cm, then the length of AC is equal to
26. If D, E and F are the mid points of BC, CA and AB respectively of the ΔABC. The ratio of area of the parallelogram DEFB and area, of the trapezium CAFD is:
27. At least two pairs of consecutive angles are congruent in a . . . . . . . .
28. Two circles having radii $$r$$ units intersect each other in such a way that each of them passes through the centre of the other. Then the length of their common chord is
29. In the given figure, ABC is a right-angled triangle. ∠ABC = 90° and ∠ACB = 60°. If the radius of the smaller circle is 2 cm, then what is the radius (in cm) of the larger circle?
30. AB and CD are two chords in a circle with centre O and AD is a diameter. AB and CD produced meet at a point P outside the circle. ∠APD = 25° and ∠DAP = 39°, then the measure of ∠CBD is:
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