Q. 1 In a circle with centre O, AD is a diameter, and AC is a chord. B is a point on AC, such that OB = 5 cm and ∠OBA =60°. If ∠DOC = 60°, then what is the length of BC?

Q. 3 The sides AB and AC of ΔABC are produced to point D and E, respectively. The bisectors of ∠CBD and ∠BCE meet at P. If ∠A = 72°, then the measure of ∠P is

Q. 4 In ΔABC, D is a point on side AB such that BD = 2 cm and DA = 3 cm. E is a point on BC such that DE||AC, and AC= 4 cm. Then (Area of ΔBDE) : (Area of trapezium ACED) is:

Q. 5 The radius of two concentric circles are 15 cm and 9 cm. What is the length of the chord of the larger circle which is tangent to the smaller circle?

Q. 6 In triangle ABC, D and E are the points on sides AB and AC, respectively, such that DE|| BC. If DE : BC =3 : 5, then (Area of triangle ADE) : (Area of quadrilateral DECB) is

Q. 8 Two circles of radii 15 cm and 12 cm intersect each other, and the length of their common chord is 18 cm. What is the distance (in cm) between their centres?

Q. 11 In ΔABC, D and E are the points on sides AC and AB, respectively, such that ∠ADE = ∠B. If AD = 7.6 cm, AE = 7.2 cm, BE = 4.2 and BC = 8.4 cm, then DE is equal to

Q. 12 PAT is a tangent to a circle at point A on it, and AB is a chord such that ∠BAT = 72°. If C is a point on the circle such that ∠CBA = 58°, then what is the measure of ∠CAB?

Q. 13 The vertices A, B, C, and D of a quadrilateral ABCD lie on a circle. ∠A is thrice ∠C and ∠D is twice ∠B. What is the difference between the measures of ∠B and ∠C?

Q. 15 A circle is inscribed in a quadrilateral ABCD, touching sides AB, BC, CD and DA at P, Q, R and S, respectively. If AS= 8 cm, BC = 11 cm, and CR = 5 cm, then the length AB is equal to