Home
Class 11
MATHS
In a triangle A B C , right angled at A ...

In a triangle `A B C ,` right angled at `A ,` on the leg `A C` as diameter, a semicircle is described. If a chord joins `A` with the point of intersection `D` of the hypotenuse and the semicircle, then the length of `A C` is equal to (a)`(A B.A D)/(sqrt(A B^2+A D^2))` (b) `(A B.A D)/(A B+A D)` (c)`sqrt(A B.A D)` (d) `(A B.A D)/(sqrt(A B^2-A D^2))`

Promotional Banner

Similar Questions

Explore conceptually related problems

In a scalene triangle A B C ,D is a point on the side A B such that C D^2=A D D B , sin s in A S in B=sin^2C/2 then prove that CD is internal bisector of /_Cdot

Line segments A C and B D are diameters of the circle of radius one. If /_B D C=60^0 , the length of line segment A B is_________

Let aa n db represent the lengths of a right triangles legs. If d is the diameter of a circle inscribed into the triangle, and D is the diameter of a circle circumscribed on the triangle, the d+D equals. (a) a+b (b) 2(a+b) (c) 1/2(a+b) (d) sqrt(a^2+b^2)

In triangle A B C ,D is on A C such that A D=B C=D C ,/_D B C=2x ,a n d/_B A D=3x , all angles are in degrees, then find the value of xdot

If a, b, c, d are in G.P., then (a + b + c + d)^(2) is equal to

If asinx+bcos(x+theta)+bcos(x-theta)=d , then the minimum value of |costheta| is equal to (a) 1/(2|b|)sqrt(d^2-a^2) (b) 1/(2|a|)sqrt(d^2-a^2) (c) 1/(2|d|)sqrt(d^2-a^2) (d) none of these

In an acute triangle A B C if sides a , b are constants and the base angles Aa n dB vary, then show that (d A)/(sqrt(a^2-b^2sin^2A))=(d B)/(sqrt(b^2-a^2sin^2B))

A circle is inscribed in a triangle A B C touching the side A B at D such that A D=5,B D=3,if/_A=60^0 then length B C equals. 9 (b) (120)/(13) (c) 13 (d) 12

In A B C with fixed length of B C , the internal bisector of angle C meets the side A Ba tD and the circumcircle at E . The maximum value of C D.D E is c^2 (b) (c^2)/2 (c) (c^2)/4 (d) none of these

Let A B C be a triangle with A B=A Cdot If D is the midpoint of B C ,E is the foot of the perpendicular drawn from D to A C ,a n dF is the midpoint of D E , then prove that A F is perpendicular to B Edot