You have triangle triangle ABC which is orthogonal angle C=90^circ with circle with center O inscribed in it. Find angle angle MCN.

motsetjela

motsetjela

Open question

2022-08-13

You have triangle A B C which is orthogonal C = 90 o with circle with center O inscribed in it. If KL is the diameter, KL∥AB, K M A B and L N A B. Find angle M C N.

Answer & Explanation

Isaias Archer

Isaias Archer

Beginner2022-08-14Added 11 answers

Step 1

If r is the inradius, please note that C S = K M = r , C T = L N = r.
Also note that P S = P K and Q T = Q L.
So we have P C = P M , Q C = Q N.
Step 2
That makes P C M and Q C N isosceles triangles.
As B Q N = A , B C N = A 2
And as A P M = B , A C M = B 2
M C N = 45 0
Roderick Bradley

Roderick Bradley

Beginner2022-08-15Added 3 answers

Step 1
It's apparent that | O M | = | O N | = | O C | ( = 2 | O K | ) and that M O N = 90 .
Step 2
Then by the inscribed angle theorem, M C N = 45 .

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