ANGLE PROPERTIES ANSWER ALL QUESTIONS

1. In the figure below POR and S are points on the circumference of a circle centre O. The point TSO and Q lie on a straight line MPT is a tangent to the circle at P. 120% Find the values of the following angles stating reasons in each case. (a) ZSRP (2mks) (b) ZORP (2mks) (c) ZRPT (2mks) (d) ZSTP (2mks) (e) ZOPM (2mks) 2. In the figure below, TA is a tangent to the circle ABCD with centre O. Z TAD = 480 and _ BOD = 1160 489 B D T Giving reasons calculate: a) ZACD (2mks) b) ZABO (2mks) c) ZADO (2mks) d) ZACB (2mks) e) ZATB (2mks) 3. In the figure below AB = 8cm and O is the centre of the circle. Determine the area of the circle if ZOAB = 15" (3mks) 15' A 8 cm R S The figure above is a cyclic quadrilateral PORS. Given that TPX is a tangent at P and O is the centre of the circle and that RQX is a straight line with ZRPQ = 50" and ZPRS = 25", giving reason in each case find: (a) angle PRO (b) angle PSR (2mks) angle PXO (2mks) angle TPS (2mks) angle POS (2mks) (2mks)5. In the figure below ABCD is a circle with centre O. AB and DC meet at a point E outside the circle. DC = BC and ZBCE= 48' E D Find the angles a) BAD (1mk) b) BDC (1mk) C) BEC (1mk) 6. In the figure O and P are centres of intersecting circles ABD and DBC respectively. Line ABE is a tangent to circle BCD at B and angle BCD = 42". A Giving reasons determine the size of: (a) Angle CBD. (2mks) (b) Angle ODB. (2mks) (c) Angle BAD. (2mks) (d) Angle ABD (2mks) (e) Angle ODA. (2mks) 7. In the figure below, O is the centre of the circle. Express the angle W in terms of angles p and q. (2mks) 8. Two circles of radii 4cm and 6cm intersect as shown below. If angle XBY = 30" and angle XAY = 97.2". Find the area of the shaded part. (Take = 7 22 )15 A 4. S P The figure above is a cyclic quadrilateral PQRS. Given that TPX is a tangent at P and O is the centre of the circle and that RQX is a straight line with ZRPQ = 50" and ZPRS = 25", giving reason in each case find: a angle PRQ (2mks) b) angle PSR (2mks) (c) angle PXQ (2mks) d) angle TPS (2mks) e) angle POS (2mks) 5. In the figure below ABCD is a circle with centre O. AB and DC meet at a point E outside the circle. DC = BC and ZBCE= 48 Find the angles a) BAD (1mk) b) BDC (1mk) c) BEC (1mk) 6. In the figure O and P are centres of intersecting circles ABD and DBC respectively. Line ABE is a tangent to circle BCD at B and angle BCD = 42". A Giving reasons determine the size of: (a) Angle CBD. (2mks) (b) Angle ODB. (2mks) (c) Angle BAD (2mks) (d) Angle ABD (2mks) (e) Angle ODA. (2mks) 7. In the figure below, O is the centre of the circle. Express the angle W in terms of angles p and q. (2mks) 8. Two circles of radii 4cm and 6cm intersect as shown below. If angle XBY = 30" and angle XAY = 97.2". Find the area of the shaded part. (Take = 7 22 ) 9. In the diagram, O is the centre of the circle and AD is parallel to BC. If angle ACB =50"