cho (P) y = -x2
a) tìm tap hop cac diem M sao cho tu do co the ke duoc 2 duong thang vuong goc voi nhau và tiep xuc (P)
b) tìm tren (P) cac diem sao cho khoang cach toi goc toa do bang \(\sqrt{2}\)
bai 1co tam giac abc can tai a tren tia doi cua cac tia bc va cb lay hai diem d va e sao cho ce = bd goi m la trung diem cua bc tu b va c ke bh vuong goc voi ad va ck vuong goc voi ae .cm 3 dt bh ck va am cung di qua mot diem
bai 2 cho tam giac abc vuong tai a goc c bang 30 do duong cao ah tren doan hc lay diem d sao cho hd=hb tu c ke ce vuong goc voi ad cmr
a, tam giac abd deu
b,eh song song voi ac
bai 3 cho tam giac abc co goc a = 90 do qua a ke dt d tu b va c ke bd vuong goc voi dt d va ce vuong goc voi dt d tinh do dai de theo bd va ce
bai 4 cho tam giac abc vuong tai a hai duong phan giac bm va cn tu m va n ke mmphay va nnphay vuong goc voi bc cmr goc mphayanphay bang 45 do
cho tam giac vuong ABC co canh goc vuong AB = 40 cm . tren canh AC lay mot diem M sao cho AM bang 1/4 canh AC .tu M ke duong thang vuong goc voi AC va cat canh BC tai diem N . tinh do dai doan thang MN
cho goc bet xoy ve tia oy sao cho xy = 5/4 yoz
a, tinh xoy va yoz
b ke tia ot sao cho toy = 80 do tia oy co la tia phan giac cua toz ko vi sao
c , qua o ke them 20 duong thang nua sao cho cac duong thang nay deu ko chua cac tia ox,oy,oz ve duong tron tam o ban kinh r goi a la tap hop cac giao diem cua duong tron noi tren voi cac goc co o trong hinh ve .tinh so tam giac ma cac dinh cua no deu thuoc tap hop a
cho goc bet xoy ve tia oy sao cho xoy = 5/4 yoz
a, tinh xoy va yoz
b, ke tia ot sao cho toy = 80 do tia oy co la tia phan giac cua toz ko? vi sao ?
c , qua o ke them 20 guong thang nua sao cho cac duong thang nay deu ko chua cac tia ox,oy,oz ve duong tron tam o ban kinh r goi a la tap hop cac giao diem cua duong tron noi tren voi cac goc o co trong hinh ve tinh so tam giac ma cac dinh cua no deu thuoc tap hop a
bai 1:Cho duong tron tam O, day AB. cac tiep tuyen ke tu A,B cat nhau tai C. ke day CD cua duong tron co duong kinh OC(D khac A,B). CD cat cung nho AB cua (O) tai E (E nam giua C va D).Chung minh:
a/goc BED= goc DAE
b/DE^2=DA*BD
bai 2:Cho tam giac ABC deu noi tiep duong tron tam O. M la diem nam tren cung nho AB. chung minh:
a/MB+MA=MA
b/ke MH vuong goc voi BC, MI vuong goc voi AB, MK vuong goc voi AC. chung minh 3 diem H,I,K thang hang
cho diem M thuoc duong thang xy . Ten tia Mx lay diem B sao cho MB bang 3cm , tren tia My lay diem C sao cho MC bang 2cm
a. tinh do da doan BC
b. goi O la mot diem nam ngoai duong thang BC . Ke cac doan thang OB , OC , OM . Biet goc BOC bang 90 do, goc BOM bang 60 do . Tinh goc MOC
cho hai duong thang xx' va yy' cat nhau tai O
a) cm hai tia phan giac Ot , Ot' cua mot cap goc ke bu tao thanh mot goc vuong
b)cm neu M thuoc duong thang Ot' thi M cach deu hai duong thang xx' va yy'
c) cm neu M cach deu hai duong thang xx' va yy' thi M thuoc duong thang Ot hoac thuoc duong thang Ot'
d)Khi M=O thi cac khoang cach tu M den xx' va yy' bang bao nhieu
e)em co nhan xet gi ve tap hop cac diem cach deu hai duong thang cat nhau xx' va yy'
cho goc bet xoy ve tia oy sao cho xy = 5/4 yoz
a, tinh xoy va yoz
b ke tia ot sao cho toy = 80 do tia oy co la tia phan giac cua toz ko vi sao
c , qua o ke them 20 guong thang nua sao cho cac duong thang nay deu ko chua cac tia ox,oy,oz ve duong tron tam o ban kinh r goi a la tap hop cac giao diem cua duong tron noi tren voi cac goc o co trong hinh ve tinh so tam giac ma cac dinh cua no deu thuoc tap hop a
mai nop roi
mong giai gium
giot toan
cho duong tron (O;R) va duong thang d co dinh khong cat duong tron.tu mot diem A bai ki tren duong thang d ke tiep tuyen AB voi duong tron (B la tiep diem ).tu B ke duong thang vuong goc voi Ao tai H tren tia doi cua tia BH lay C sao cho HC=HB.
a,chung minh C thuoc duong tron (O;R) va AC la tiep tuyen cua (O;R).
b,tu Oke duong thang vuong goc voi duong thang d tai i,OI cat BC tai K.chung minh OH.OA=OI.OK=R^2
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