Multiple Choice QuestionsIn Fig., a circle touches the side DF of EDF at H and touches ED and EF produced at K and M respectively. If EK = 9 cm, then the perimeter of EDF (in cm) is:
18
13.5
12
9
Short Answer TypeTangents PA and PB are drawn from an external point P to two concentric circle with centre O and radii 8 cm and 5 cm respectively, as shown in Fig., If AP = 15 cm, then find the length of BP.
Given: Tangents PA and PB are drwan from an external point P to two
concentric circles with centre O and radii OA = 8 cm, OB = 5 cm
respectively. Also, AP = 15 cm.
Construction: We join the points O and P.
Proof: OA AP ; OB BP
[ Using the property that radius is perpendicular to the tangent at the
point of contact of a circle.]
In right angled triangle OAP,
OP2 = OA2 + AP2 [ Using pythagoras theorem ]
= (8)2 + ( 15 )2 = 64 + 225 = 289
OP = 17 cm
In right angled triangled OBP,
OP2 = OB2 + BP2
BP2 = OP2 - OB2
(17)2 - (5)2
289 - 25
= 264
BP = = 2 cm.
Long Answer TypeIn fig., an isosceles triangle ABC, with AB =AB, circumscribes a circle. Prove that the point of contact P bisects the base BC.
OR
In fig., the chord AB of the larger of the two concentric circles, with centre O, touches the smaller circle at C. Prove that AC = CB.
Prove that the parallelogram circumscribing a circle is a rhombus.
OR
Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
OR
A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.
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