Reference no: EM132387066

Question 1: In the adjoining figure, two tangents RO and RP are drawn from an external point R to the circle with centre O.  If ∠PRQ 120°, then prove that OR = PR + RQ.

Question 2: In the adjoining figure, AP and BP are tangents to a circle with centre O such that AP = 5 cm and ∠APB = 60°. Find the length of chord AB.

Question 3: In the adjoining figure, from an external point P, two tangents PT and PS are drawn to a circle with centre O and radius r. If OP = 2r, show that ∠OTS = ∠OST = 30°.

Question 4: In the adjoining figure, XP and XQ are tangents from X to the circle with centre O. R is a point on the circle.

Prove that XA + AR = XB + BR.

Question 5: A circle is touching the side BC of a Δ ABC at P and is touching AB and AC when produced at Q and R respectively. Prove that AQ = 1/2 (perimeter of Δ ABC )

Question 6: Prove that the angle between the two tangents to a circle drawn from an external point, is, supplementary to the angle subtended by the line segment joining the points of contact at the centre.C

Question 7: In the adjoining figure, a quadrilateral ABCD is drawn to circumscribe a circle, Prove that AB + CD = AD + BC

Question 8: In the adjoining figure, a triangle is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D are the lengths 4 cm and 3 cm respectively. If area of Δ ABC is 21 cm², find the lengths of sides AB and AC.

Question 9: Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

Attachment:- circle figures.rar