In acute angled triangle `A B C ,A D` is the altitude. Circle drawn with `A D` as its diameter cuts `A Ba n dA Ca tPa n dQ ,` respectively. Length of `P Q` is equal to `/(2R)` (b) `(a b c)/(4R^2)` `2RsinAsinBsinC` (d) Δ`/R`

In triangle A B C ,A D is the altitude from Adot If b > c ,/_C=23^0,a n dA D=(a b c)/(b^2)-c^2, then /_B=_____

A B C is an equilateral triangle of side 4c mdot If R , r, a n d,h are the circumradius, inradius, and altitude, respectively, then (R+r)/h is equal to (a) 4 (b) 2 (c) 1 (d) 3

In A B C , A D and B E are altitudes. Prove that (a r( D E C))/(a r( A B C))=(D C^2)/(A C^2)

In Figure, triangle A B C is drawn to circumscribe a circle of radius 4cm such that the segments B Da n dD C are of lengths 8cm and 6cm respectively. Find the lengths of sides A Ba n dA C , when area of A B C is 84 c m^2dot

A D ,\ B E\ a n d\ C F , the altitudes of A B C are equal. Prove that A B C is an equilateral triangle.

A D ,\ B E\ a n d\ C F , the altitudes of A B C are equal. Prove that A B C is an equilateral triangle.

If A B C is a right triangle right-angled at Ba n dM ,N are the mid-points of A Ba n dB C respectively, then 4(A N^2+C M^2)= (A) 4A C^2 (B) 5A C^2 (C) 5/4A C^2 (D) 6A C^2

In A B C ,/_A=90^0a n dA D is an altitude. Complete the relation (B D)/(D A)=(A B)/(()) .

In Figure, A D\ a n d\ B E are respectively altitudes of an isosceles triangle A B C with A C=B Cdot Prove that A E=B D

In a right triangle A B C right-angled at B , if P a n d Q are points on the sides A Ba n dA C respectively, then (a) A Q^2+C P^2=2(A C^2+P Q^2) (b) 2(A Q^2+C P^2)=A C^2+P Q^2 (c) A Q^2+C P^2=A C^2+P Q^2 (d) A Q+C P=1/2(A C+P Q)dot