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In isosceles △ ABC, ab = AC = 13cm, BC = 10cm. Find the radius of the circumcircle of isosceles △ ABC
Let o be the center of △ ABC circumscribed circle, connect Ao, and extend Ao to meet BC to D, connect OB and OC, ∵ AB = AC, o be the center of △ ABC circumcircle, ∵ ad ⊥ BC, BD = DC (three lines in one), BD = DC = 12 BC = 5, let the radius of the isosceles △ ABC circumcircle be r, then OA = ob = OC = R, in RT △ abd, by Pythagorean Theorem
As shown in the figure, ⊙ o is the circumcircle of ⊙ ABC, and ab = AC = 13cm, BC = 24cm, then the radius of ⊙ o is______ .
In RT △ ACD, ∵ AC = 13, CD = 12, OC = 12, in RT △ ACD, ∵ AC = 13, CD = 12, ad = 132 − 122 = 5, if the radius of ⊙ o is r, then in RT △ OCD, OD = R-5, CD = 12, OC = R ∵ 2 + 122 = R
In isosceles △ ABC, ab = AC = 13cm, BC = 10cm. Find the radius of the circumcircle of isosceles △ ABC
Let o be the center of △ ABC circumscribed circle, connect Ao, and extend Ao to meet BC to D, connect OB and OC, ∵ AB = AC, o be the center of △ ABC circumcircle, ∵ ad ⊥ BC, BD = DC (three lines in one), BD = DC = 12 BC = 5, let the radius of the isosceles △ ABC circumcircle be r, then OA = ob = OC = R, in RT △ abd, by Pythagorean Theorem
In isosceles △ ABC, ab = AC = 13cm, BC = 10cm. Find the radius of the circumcircle of isosceles △ ABC
Let o be the center of △ ABC circumscribed circle, connect Ao, and extend Ao to meet BC to D, connect OB and OC, ∵ AB = AC, o be the center of △ ABC circumcircle, ∵ ad ⊥ BC, BD = DC (three lines in one), BD = DC = 12 BC = 5, let the radius of the isosceles △ ABC circumcircle be r, then OA = ob = OC = R, in RT △ abd, by Pythagorean Theorem
If the waist length of the isosceles triangle ABC is 10 cm and the base length is 16 cm, then the height on the bottom edge is -, the area is -, and the height on the waist is——
Then the height on the bottom edge is √ [10 ^ 2 - (16 / 2) ^ 2] = 6cm
So the area is s = (1 / 2) * 16 * 6 = 48CM ^ 2
If you don't understand, I wish you a happy study!
If the isosceles triangle ABC is inscribed on a circle with a radius of 10 cm and the length of its bottom edge BC is 16 cm, then s △ ABC is More details, better with a picture
In the first case, the center of the circle O is in the triangle ABC, connecting Ao, and extending Ao to meet BC at D. therefore, the oblique edge of the right triangle ODC is 10, and one right angle side is 8. Therefore, OD = 6, the height of BC side ad = 10 + 6 = 16, ﹤ s △ ABC = 1 / 2 * BC * ad = 1 / 2 * 16 * 16 = 128. In the second case, the center O is outside the triangle, and the height is 10-6 = 4, ﹤ s △ ABC
In the isosceles triangle ABC, if AB = AC = 117cm, BC = 16cm, then the area of △ ABC
Ad ⊥ BC. ∵ ABC is isosceles triangle ᙽ BD = CD = 8cm (three lines in one isosceles triangle) in RT △ abd, ad = ab ⊥ BD ∵ 117 ⊥ 8 ∵ s = 1 / 2 * ad * BC = 8 roots (125 * 109) = 40 roots 545, which was hard worked out by ourselves
If the waist length ab of the isosceles △ ABC is 10 cm and the bottom BC is 16 cm, then the height on the bottom edge is______ .
As shown in the figure, ∵ AB = AC = 10cm, ad ⊥ BC,
∴BD=CD=1
2BC=8cm，
In RT △ abd, according to Pythagorean theorem, ad is obtained=
AB2−BD2=6cm．
So the answer is: 6cm
If the isosceles triangle ABC is inscribed with a circle with a radius of 10 cm, the length of its bottom edge BC is 16 cm. Calculate the area of triangle ABC
If the midpoint of BC is D, then ad is the center of the circle O of the vertical bisector of BC. On ad, Bo = 10cmbd = 16 △ 2 = 8cmod = √ (Bo? - BD?) = 6cmad = Ao + od = 10 + 6 = 16cms ⊿ ABC = half BC × ad = half × 16 × 16 = 128cm ⊿ on AD
As shown in the figure, in isosceles △ ABC, ab = AC, ad is the height on the bottom edge. If AB = 10cm, BC = 12cm, then ad=______ cm．
∵ isosceles △ ABC, ab = AC, ad is the height on the bottom edge,
∴BD=CD，
∵BC=12cm，
∴BD=cm，
∵ △ ADB is a right triangle, ab = 10cm
∴AD=
AB2−BD2=
102−62=8cm，
So the answer is 8cm
RELATED INFORMATIONS
- 1. If the circumference of the isosceles △ ABC is 10 cm, the bottom edge length is y cm, and the waist length is x cm, then the value range of waist length x is______ .
- 2. In the triangle ABC, ab = AC, the center line be of triangle ABC divides the circumference of triangle into two parts of 9cm and 12cm, and calculates the length of BC in triangle ABC You have to draw your own pictures, The length of the center line is also included in the perimeter of the two parts
- 3. Given that the circumference of the isosceles triangle ABC is 40cm, ad is the height on the bottom edge, and the circumference of the triangle abd is 30cm, what is the length of ad
- 4. As shown in the figure, in the isosceles triangle ABC, ab = AC, point D is a point on BC, de ∥ AC intersects AB at point E, DF ∥ AB intersects AC at point F, ① As shown in Figure 1, when point D is on BC, there is de + DF = AB, please explain the reason. ② as shown in Figure 2, when point D is on the extension line of BC, please refer to figure 1 to draw the correct figure, write down the relationship between De, DF and AB, and write the proof process,
- 5. It is known that Mn is the vertical bisector of line AB, and C and D are two points on Mn (1) Δ ABC, △ abd are isosceles triangles; （2）∠CAD=∠CBD．
- 6. As shown in the figure, given that AB is 2cm longer than AC, the vertical bisector of BC intersects AB at D, crosses BC at e, and the circumference of △ ACD is 14cm, then ab=______ cm，AC=______ cm．
- 7. As shown in the figure: the circumference of △ ABC is 24cm, ab = 10cm, the vertical bisector De of edge AB intersects BC, the edge is at point E, and the perpendicular foot is D, calculate the circumference of △ AEC
- 8. As shown in the figure, it is known that in trapezoidal ABCD, BD bisection ∠ ABC, ∠ a = 120 ° and BD = BC = 4 3, then s trapezoid ABCD = () A. 4 Three B. 12 C. 4 3-12 D. 4 3+12
- 9. In △ ABC, ab = 4 3，AC=2 3, ad is the center line of BC side, and ∠ bad = 30 °, then BC=______ .
- 10. In the isosceles triangle ABC, the vertical bisector of one waist AB intersects the other waist AC at g. given AB = 10, the circumference of triangle GBC is 17, then the length of bottom BC is?
- 11. Are two right triangles with an angle of 60 ° congruent? Are two isosceles triangles congruent with an obtuse angle
- 12. The method of drawing auxiliary line in the proof of congruent triangle
- 13. Can I divide two triangles with 24 ', 84' and 104 ', 52' angles into two isosceles triangles with a straight line (if yes, please write down the divided? B If you can, write the top angle readings of the two isosceles triangles
- 14. The area and perimeter of an congruent triangle are equal. Are the two triangles with the same area and perimeter congruent triangles?
- 15. The isosceles triangle ABC with base BC is still isosceles triangle after being divided into two smaller triangles by a line passing through a vertex Draw all the situations and mark the angles
- 16. In the triangle ABC, ab = AC, the line passing through a vertex intersects the opposite side of D. the line divides the original triangle into two isosceles triangles In the triangle ABC, ab = AC, the line passing through a vertex intersects the opposite side of D. the line divides the original triangle into two isosceles triangles. Find the degree of the three inner angles of the triangle ABC.
- 17. The degree of the top angle of an isosceles triangle is four times that of the base angle. How many degrees are the base angle and the top angle of the isosceles triangle? What triangle is this?
- 18. If an interior angle of an isosceles triangle is 80 degrees, how many degrees or degrees does the top angle differ from the base angle?
- 19. For an isosceles triangle with a vertex angle of 30 degrees, if the waist length is 2, then the height () on the waist is () and the area of the triangle is ()
- 20. The top angle of an isosceles triangle is 43 degrees. What is its base angle?