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square ABCD, M is the midpoint of AD and N is the
midpoint of MD. Prove that ∠NBC = 2∠ABM.
2.(CHINA/1995) In △ABC, ∠A = 90
°
;AB = AC, D is a
point on BC. Prove that BD
2
+ CD
2
= 2AD
2
.
that Rt△ABC has a perimeter of 30 cm and an area
of 30 cm
2
. Find the lengths of its three sides.
4. In the Rt△ABC, ∠C = 90
°
, AD is the angle bisector of∠
A which intersects BC at D. Given AB = 15 cm, AC = 9 cm,
Find the distance of D from AB.
the right triangle ABC, ∠C = 90
°
,BC = 12 cm, AC = 6
cm, the perpendicular bisector of AB intersects AB and BC at
D and E respectively. Find CE.
6. In the rectangle ABCD, CE ⊥ DB at E, BE =
1
4
BD and
CE = 5 cm. Find the length of AC.
7: In △ABC, ∠C = 90
°
, D is the mid-point of AC. Prove
that AB
2
+ 3BC
2
= 4BD
2
:
8: In the right triangle ABC, ∠C = 90°, E、D are points on
AC and BC respectively. Prove that AD
2
+ BE
2
= AB
2
+ DE
2
:
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