Lengths of Tangents Drawn from External Point
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O is any point inside a rectangle ABCD. Prove that OB2+OD2=OA2+OC2.
circles of radii touch each other externally and have axis as a common tangent then
are in A.P
are in A.P
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If angle between two tangents drawn from a point P to a circle of radius a and centre O is 60∘ , then OP = a √3.
In Fig. 8.63, AB is a chord of length 16 cm of a circle of radius 10 cm. The tangents at A and B intersect at a point P. Find the length of PA.
In Fig. 8.61, a circle is inscribed in a quadrilateral ABCD in which ∠B=90∘. If AD =23 cm, AB =29 cm and DS =5 cm, find the radius r of the circle.
In the given figure, the incircle of △ABC touches the sides AB, BC and CA at the points P, Q, R respectively. Show that
AP+BQ+CR=BP+CQ+AR
=12 (Perimeter of △ABC)
[3 MARKS]
A circle is inscribed in ΔABC touching the sides AB, BC and CA at points D, E and F respectively. If AB= 10 cm, BC = 12 cm and CA = 8 cm, then the lengths of AD, BE and CF respectively will be
3cm, 7cm and 5cm
4cm, 6cm and 8 cm
2cm, 6cm and 7cm
5cm, 9cm and 4cm
From an external point P, tangents PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn, which intersects PA and PB at C and D respectively. If PA=14cm, find the perimeter of ΔPCD.
In the given figure, a circle touches all the four sides of a quadrilateral ABCD whose three sides are AB = 6 cm, BC = 7 cm and CD = 4 cm. Find AD.
In the given figure, a triangle PQR is drawn to circumscribe a circle of radius 6 cm such that the segments QT and TR into which QR is divided by the point of contant T, are of lengths 12 cm and 9 cm respectively. If the area fo \Delta PQR = 189 cm^2 then the length of side PQ is
(a) 17.5 cm (b) 20 cm (c) 22.5 cm (d) 25 cm
In figure, PA and PB are tangents to the circle from an external point P. CD is another tangent touching the circle at Q. If PA = 12 cm, QC = QD = 3 cm, then find PC + PD.
(a)
(b) 231 cm2
(c) 462 cm2
(d) 924 cm2