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
A.
18
It is known that the tangents from an external point to the circle are equal.
EK = EM, DK = DH and FM = FH .....(1)
Perimeter of EDF = ED + DF + FE
= (EK - DK) + (DH + HF) + EM - FM)
= (EK - DH) + (DH + HF) + (EM - FH) [Using (1)]
= EK + EM
= 2EK = 2(9 CM) = 18 CM
Hence, the perimeter of EDF is 18 cm.
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.
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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