In the given figure. A is the centre of the circle , ABCD is a parallelogram and CDE is a straight line.
Prove that `: angle BCD = 2 angle ABE `
` (##SEL_RKB_ICSE_MAT_X_C17_E02_036_Q01.png" width="80%">

Calculate the angles x,y and z if (x)/(3) = (y)/(4) =(z)/(5) (##SEL_RKB_ICSE_MAT_X_C17_E02_042_Q01.png" width="80%">

In the followoing figure , AD is the diameter of the circle with centre O. Chords AB,BC and CD are equal .If angle DEF = 110 ^(@) , Calculate : (i) angle AEF . (ii) angle FAB (##SEL_RKB_ICSE_MAT_X_C17_E03_002_Q01.png" width="80%">

The given figures shows a circle with centre O. Also , PQ = QR = RS and angle PTS = 75^(@) Calculate: (i) agnle POS (ii) angle QOR (iii) angle PQR (##SEL_RKB_ICSE_MAT_X_C17_E03_004_Q01.png" width="80%">

Two unequal circles with centres A and B intersect each other at points C and D. The centre B of the smaller circles lies on the circumference of the bigger circle with centre A. If angle CMD = x^(@) , find in terms of x, the measure of angle DAC . (##SEL_RKB_ICSE_MAT_X_C17_E01_013_Q01.png" width="80%">

In the given figure angle BAD = 60 ^(@) ,angle ABD = 70^(@) angle BDC = 45^(@) (i) prove that AC is a diameter of the circle (ii) Find angle ACB (##SEL_RKB_ICSE_MAT_X_C17_E02_002_Q01.png" width="80%">

In the following figure , angle B = 90 ^(@) angle ADB = 30 ^(@) and angle ACB = 60 ^(@) If angle CD = m find AB . (##SEL_RKB_ICSE_MAT_IX_CR_02_E01_162_Q01.png" width="80%">

In the given figure ,I is the incentre of triangle ABC . AI produced meets the circumcircle of the triangle ABC at point D. if angle BAC = 50^(@) and angle ABC = 70 ^(@) , find : (i) angle BCD (ii) angle ICD (iii) angle BIC (##SEL_RKB_ICSE_MAT_X_C17_E01_015_Q01.png" width="80%">

In the following figure . (i) if angle BAD = 96^(@) , " find " angle BCD and angle BFE. (ii) Prove that AD is parallel to PE. (##SEL_RKB_ICSE_MAT_X_C17_E02_019_Q01.png" width="80%"> (b) ABCD is a parallelogram. A circle through vertices A and B meets side BC at point P and side AD at point Q . Show that quadrilateral PCDQ is cyclic.