7/23/2019 UNit-10 eng 3

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UNIT-10 TEST-7

1/02/2015

Note:- Each and every question have 5 marks

Max. Marks - 50

1. In the given fg (1) OP is equal to the diameter o the circle with centre O. Prove thatABP is an equilateral triangle.

2. In the given fg (2) AB A!" # is the mid$%oint o A!" B# is the diameter o the circle"then %rove that A& 1' A!.

. I PAB is a secant to a circle intersecting it at A and B and P* is a tangent then PA.PB P*2.. In fgure () !hords AB and !# intersect at P. I AB +cm" PB cm and P# cm.

,ind the length o !#.+. In the fgure ()" AB! is an isosceles triangle in which AB A!. A circle through B

touches the side A! at # and intersect the side AB at P. I # is the mid%oint o side A!"*hen AB AP.

-. In fgure (+) and m are two %arallel tangents at A and B. *he tangent at ! maes aninterce%t #& /etween the tangent l and m. Prove that 0#,&3

4. In the given fgure (-) *A5 is a tangent to the circle" with centre O" at the %oint A. I0OBA23" fnd the value o 6 and 7.

8. In the given fgure (4). 0! is right angle o 9AB! . A semicircle is drawn on AB asdiameter. P is an7 %oint on A! %roduced. :hen ;oined" BP meets the semi$circle in %oint#. Prove that" Prove that< (i) 0P>*0P*> (ii) P* P>

1. *wo tangents PA and PB are drawn to a circle with centre O (fg. ) rom an e6ternal%oint P. Prove that APB 2 OAB

CGI TET !"!E#