11. In ΔABD, C is the midpoint of BD. If AB = 10 cm, AD = 12 cm and AC = 9 cm, then BD = ?
12. In ΔABC, the perpendiculars drawn from A, B and C meet the opposite sides at points D, E and F respectively. AD, BE and CF intersect at point P. If ∠EPD = 110° and the bisectors of ∠A and ∠B meet at point Q, then ∠AQB = ?
13. The tangent at a point A of a circle with centre O intersects the diameter PQ of the circle (when extended) at the point B. If ∠BAP = 125°, then ∠AQP is equal to:
14. Two circles touch each other at point X. A common tangent touch them at two distinct points Y and Z. If another tangent passing through X cut YZ at A and XA = 16 cm, then what is the value (in cm) of YZ?
15. ABCD is a cyclic quadrilateral. Side AB and DC, when produced, meet at E and sides AD and BC when produced, meet at F. If ∠ADC = 76° and ∠AED = 55°, then ∠AFB is equal to:
16. ΔABC, AB = 20 cm, BC = 7 cm and CA = 15 cm. Side BC is produced to D such that ΔDAB ∽ ΔDCA. DC is qual to:
17. If the angle between two radii of a circle be 130°, then the angle between the tangents at the end of these radii (in degrees) is:
18. PQR is a triangle such that PQ = PR. RS and QT are the median to the sides PQ and PR respectively. If the medians RS and QT intersect at right angle, then what is the value of $${\left( {\frac{{{\text{PQ}}}}{{{\text{QR}}}}} \right)^2}?$$
19. ΔABC is isosceles having AB = AC and ∠A = 40°. Bisectors PO and OQ of the exterior angles ∠ABD and ∠ACE formed by producing BC on both sides, meet at O. Then the value of ∠BOC is
20. ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If the area of triangle ABC is 136 cm2, then the area of triangle BDE is equal to:
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