Question

opposite
Hol
ZB is a right angle in AABC. BD I AC and DE AC. IF AD = 4DC. prove that BD = 2DC
2. 5. 12, 13 are the lengths of the sides of a triangle. Show that the triangle is right angled. Find
the length of altitude on the hypotenuse.
3. In APOR, QM is the altitude to hypotenuse PR. If PM = 8, RM = 12, find PQ, QR
and QM
Nn AABC, mZB = 90, BM 1 ACME AC. If AM - MC = 7, AB2-BC2 = 175, find AC.
ZA is right angle in AABC. AD is an altitude of the triangle. If AB = 15, BD = 2, find
the length of the hypotenuse of the triangle.
6. mZB = 90 in AABC. BM is altitude to AC.
If AM - BM = 8, find AC.
If BM = 15, AC = 34, find AB.
(3) If BM = 2/30, MC = 6, find AC. If AB - VIO. AM -2.5, find MC.
7. In APQR mZQ = 90, PQ = x, QR = y and QD I PR D E PR, Find PD, OD, RD in terms
of x and y.
8. ZQ is a right angle in APQR and QM 1 PR. M € PR. If PQ - 4QR, then prove that
PM = 16RM
PORS is a rectangle. If PQ + QR = 7 and PR + QS = 10, then find the area of
PORS.
10. The diagonals of a convex ABCD intersect at right angles. Prove that
AB2 + CD2 ADP + BC2
II. In APOR, mZO - 90, ME QR and NE PQ. Prove that PM + RN? - PR? + MN2
12. The sides of a triangle have lengths a? + b2ab, 02 - b?, where a > b and a b E R+ Prove
that the angle opposite to the side having length a? + is a right angle
13. In AABC, 2B - 90 and BE is a median. Prove that ABP + BC? + AC2-SBE2
14. AB - AC and 2A is right angle in AABC I BC - 12a, then find the area of the triangle
(ae R a > 0)
153
OF PYTHAGORAS​

Answer 1

Answer:

"QM" (and any subsequent words) was ignored because we limit queries to 32 words.