### Geometry Class 9th Mathematics Term 3 Tamilnadu Board Solution

##### Question 1.O is the centre of the circle. AB is the chord and D is mid-point of AB. If the length of CD is 2cm and the length of chord is12 cm, what is the radius of the circle A. 10cmB. 12cmC. 15cmD. 18cmAnswer:In triangle AODAD = 6cmAO = rOD = OC–CD = r–2Applying Pythagoras theorem we get   r = 10cmQuestion 2.ABCD is a cyclic quadrilateral. Given that ∠ADB + ∠DAB = 120°and ∠ABC + ∠BDA = 145°. Find the value of ∠CDB A. 75°B. 115°C. 35°D. 45°Answer:As ADB + DAB = 120°In triangle ABD as sum of all angles = 180° ABD = 180–120 = 60°As ABCD is cyclic, opposite angles have sum of 180°Let BAD = x°Hence BCD = 180–xLet BDC = a°Let DBC = z°; ABC = 60 + zLet ADB = y°As sum of angles of triangle BDC = 180°180–x + a + z = 180a = x–z ...(1)According to question,x + y = 120 ..(2)and60 + z + y = 145...(3)Subtracting (3) from (2)We getx + y–60–z–y = –25x–z = 35Equating from (1) we geta = 35°hence CDB = 35°Question 3.In the given figure, AB is one of the diameters of the circle and OC is perpendicular to it through the center O. If AC is 7√2 cm, then what is the area of the circle in cm2 A. 24.5B. 49C. 98D. 154Answer:In triangle AOC AO = OC = radius of circle = rUsing Pythagoras theorem,    As area of a circle is given by = Question 4.In the given figure, AB is a diameter of the circle and points C and D are on the circumference such that ∠CAD = 30°and ∠CBA = 70° what is the measure of ACD? A. 40°B. 50°C. 30°D. 90°Answer:According to theorem the angle subtended by a diameter on the circumference of a circle is 90° ACB = 90°Angle subtended by chord AC on major segment = ABC = 70°Angle subtended on minor segment = 180–70 = 110° = ADCAs sum of angles of triangle ADC = 180° ACD = 180–30–110 = 40°Question 5.Angle in a semi circle isA. obtuse angleB. right angleC. an acute angleD. supplementaryAnswer:As a semicircle is formed by a diameter and the angle subtended on the circumference by the diameter is 90°.Question 6.Angle in a minor segment isA. an acute angleB. an obtuse angleC. a right angleD. a reflexive angleAnswer:The angle formed by a chord in the major segment is acute whereas in the minor segment is obtuse and the sum of both angles is 180°.Question 7.In a cyclic quadrilateral ABCD, ∠A = 5x, ∠C = 4x the value of x isA. 12°B. 20°C. 48°D. 36°Answer:In a cyclic quadrilateral sum of opposite angles is 180°   Question 8.Angle in a major segment isA. an acute angleB. an obtuse angleC. a right triangleD. a reflexive angleAnswer:The angle formed by a chord in the major segment is acute whereas in the minor segment is obtuse and the sum of both angles is 180°.Question 9.If one angle of a cyclic quadrilateral is 70°, then the angle opposite to it isA. 20°B. 110°C. 140°D. 160°Answer:As the sum of opposite angles in a cyclic quadrilateral is 180°Let opposite angle be x°  PDF FILE TO YOUR EMAIL IMMEDIATELY PURCHASE NOTES & PAPER SOLUTION. @ Rs. 50/- each (GST extra)

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