In the adjacent figure, it is given that AB =AC, `angleBAC = 36^(@) , angleADB = 45^(@) ` and `angleAEC = 40^(@)` . Find (i) `angleABC (ii) angleACB (iii) angleDAB (iv) angleEAC`.

In the adjacent figure, it is given that, BC || DE, angleBAC = 35^(@) and angleBCE = 102^(@) . Find the measure of (i) angleBCA (ii) angleADE and (iii) angleCED .

In the adjacent figure. AC = 6 cm, AB = 5 cm and angleBAC = 30^(@) . Find the area of the triangle.

In the given figure, ABCD is a cyclic quadrilateral where diagonals intersect at P such that angleDBC=40^(@) and angleBAC=60^(@) find (i) angleCAD (ii) angleBCD

In the abjoining figure, point O is the centre of the circle . Length of chord AB is equal to the radius of the circle . Find (i) angleAOB (ii) angleACB (iii) nm (arc AB) (iv) m (arc ACB)

In the adjoining figure, square P Q R S is a cyclic quadrilateral. Side PQ ~= side RQ. anglePSR = 110^(@) . Find (i) anglePQR (ii) m (arc PQR) (iii) m (arc QR) (iv) anglePRQ

In the adjoining figure, (i) if m (arc CE) = 54^(@) , m (arc BD) =23^(@) , then find angleCAE . (ii) If AB = 4 . 2 , BC = 5 . 4 , AE = 12, then find AD (iii) If AB 3 . 6 , AC = 9 . 0 , AD = 5 . 4 , then find AE.

In the adjoining figure, point B is the point of contact and point O is the centre of the circle. Seg OE bot se AD, if AB = 12, AC = 8, then find (i) AD (ii) DC and (iii) DE

In the adjoining figure, line PR touches the circle at point Q . Using the information given in the diagram, answer the following questions. (i) What is the sum of angleTAQ and angleTSQ ? (ii) Write names of angles congruent to angleAQP . (iii) Write names of angles congruent to angleQTS . (iv) If angleTAS= 65^@ , then find angleTQS and arc TS . (v) It angleAQR=42^(@) and angleSQR=58^(@) , then find angleATS .

Find the value of x^(2) for the given values of x. (i) x lt 3 (ii) x gt -1 (iii) x ge 2 (iv) x lt -1