OA C?

I will explain if my ans is correct. If you can post the answer with the spoiler, that would be great.

Thanks

OA is A

I was running and was thinking about the Q again and I realized that I blew it. Even though I selected C, I was doubtful. Arghhh

Here is what I think


Why A is the answer. We know that angle C =90 and that means AB is the hypotenuse. Also we know that D is the mid point of AB, Now the question is asking about the length of CD. Isn't CD the perpendicular bisector of AB? I am not sure. Just because a line segment divides another line segment into two halves does not make it perpendicular bisector. I dont think so. Can some one tell me this?

see this https://www.mathwarehouse.com/geometry/s ... heorem.php.

So that means AD/AC=BD/BC We know that AD=BD and hence AC=BC. we already know that C is 90, that means we have a right angled isosceles triangle ABC. Given that angles BCD and ACD are equal, they both have to be 45 forming another 2 45,45,90 triangles

CD may or may not be the perpendicular bisector.

Also, there is a formula which says that the median of the hypotenuse will be equidistant from the three vertices. You can reach the answer by similar triangles.

Good to know that, In a right triangle, the mid point on the hypotenuse is equidistant from the three vertices.

I don't think we can say that CD is the perpendicular bisector. If CD is the perpendicular bisector that angle is 90 and we are given in other case with B=45, which means that the triangle CDB is right angled isosceles triangle.

As the answer is not in sync with the perpendicular bisector thought, CD can't be the perpendicular bisector.

Since angle subtended by a diameter within a semicircle is always that of 90 degrees, if we assume that AB is the diameter of a circle and it extends and angle of 90 degrees on any point of the circumference, then, D being the centre of the circle, AD = BD = CD = radius = 5.

At the same time, nothing much can be derived from the measure of angle B since the point C could be at any point on the ray defining an angle of 45 degrees extending from B.

Hence the answer would be [A]

Dude you are assuming that this triangle is inscribed in a circle with diameter as AB. This will not hold true until and unless we know that DC = AD = BD or we know for sure from the question that triangle is inscribed in a circle with dia = AB