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Circles
Question
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Points A and B are on the same side of a line l. AD and BE are perpendiculars to I, meeting at D and E respectively. C is the mid-point of AB. Prove that CD = CE
[Hint: From C draw the perpendicular CM on l.]

Answer

Solution not provided.

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Some More Questions From Circles Chapter

If the diagonals of a parallelogram are equal, then show that it is a rectangle.

Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

 Show that the diagonals of a square are equal and bisect each other at right angles.

Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

Diagonal AC of a parallelogram ABCD bisects ∠A (see figure). Show that:
(i)    it bisects ∠C also
(ii)    ABCD is a rhombus.

ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D.

ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that (i) ABCD is a square (ii) diagonal BD bisects ∠B as well as ∠D.

In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see figure). Show that:

(i)    ∆APD ≅ ∆CQB
(ii)   AP = CQ
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