PQ is a chord of a circle and R is point on the minor arc. If PT is a tangent at point P such that QPT = 60 then find <PRQ. Ans. 120 If a tangent PQ at a point P of a circle of radius 5cm meets a line through the centre O at a point Q such that OQ = 12 cm then find the length of PQ. Ans. cm From a point P, two tangents PA and PB are drawn to a circle C(O,r) . If OP =2r ,then what is the type of APB. Ans. Equilateral triangle If the angle between two radii of a circle is 130,then find the angle between the tangents at the end of the radii. Ans. 50. ABCD is a quadrilateral. A circle centred at O is inscribed in the quadrilateral. If AB = 7cm , BC = 4cm , CD = 5cm then find DA. Ans. 8 cm In a ABC , AB = 8cm , ABC = 90. Then find the radius of the circle inscribed in the triangle. Ans. 2cm ( Two Marks Questions ) Two tangents PA and PB are drawn from an external point P to a circle with centre O. Prove that OAPB is a cyclic quadrilateral. If PA and PB are two tangents drawn to a circle with centre O , from an external point P such that PA=5cm and APB = 60, then find the length of the chord AB. Ans. 5cm CP and CQ are tangents from an external point C to a circle with centre O .AB is another tangent which touches the circle at R and intersects PC and QC at A and B respectively . If CP = 11cm and BR = 4cm, then find the length of BC. Ans. 7cm If all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus. Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle. In adjacent figure; AB & CD are common tangents to two circles of unequal radii. Prove that AB=CD. ( Three Marks Questions) If quadrilateral ABCD is drawn to circumscribe a circle then prove that AB+CD=AD+BC.
PQ is a chord of a circle and R is point on the minor arc. If PT is a tangent at point P such that QPT = 60 then find <PRQ. Ans. 120 If a tangent PQ at a point P of a circle of radius 5cm meets a line through the centre O at a point Q such that OQ = 12 cm then find the length of PQ. Ans. cm From a point P, two tangents PA and PB are drawn to a circle C(O,r) . If OP =2r ,then what is the type of APB. Ans. Equilateral triangle If the angle between two radii of a circle is 130,then find the angle between the tangents at the end of the radii. Ans. 50. ABCD is a quadrilateral. A circle centred at O is inscribed in the quadrilateral. If AB = 7cm , BC = 4cm , CD = 5cm then find DA. Ans. 8 cm In a ABC , AB = 8cm , ABC = 90. Then find the radius of the circle inscribed in the triangle. Ans. 2cm ( Two Marks Questions ) Two tangents PA and PB are drawn from an external point P to a circle with centre O. Prove that OAPB is a cyclic quadrilateral. If PA and PB are two tangents drawn to a circle with centre O , from an external point P such that PA=5cm and APB = 60, then find the length of the chord AB. Ans. 5cm CP and CQ are tangents from an external point C to a circle with centre O .AB is another tangent which touches the circle at R and intersects PC and QC at A and B respectively . If CP = 11cm and BR = 4cm, then find the length of BC. Ans. 7cm If all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus. Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle. In adjacent figure; AB & CD are common tangents to two circles of unequal radii. Prove that AB=CD. ( Three Marks Questions) If quadrilateral ABCD is drawn to circumscribe a circle then prove that AB+CD=AD+BC.