construct a right angled triangle ABC in which AB=6 cm, angle B = 90° and angle C =30°
Answers
Answer:
Step-by-step explanation:
1. take ab as base. Now make 90 degree angle at point B. and then draw the line through 90 degree. Now take a certain point C at BC(line u just made) and now draw the ling BA from point B. Easy.
Answer:
Step-by-step explanation:
- Consider the following situation. If a circle is drawn through B, D, and C, BC will be its diameter as ∠BDC is of measure 90∘
- The center E of this circle will be the mid-point of BC.
The required tangents can be constructed on the given circle as follows.
Step 1
Join AE and bisect it. Let F be the mid-point of AE.
Step 2
Taking F as centre and FE as its radius, draw a circle which will intersect the circle at point B and G. Join AG.
AB and AG are the required tangents.
∠AGE is an angle in the semi-circle. We know that an angle in a semi-circle is a right angle.
∴∠AGE=90∘
⇒EG⊥AG
Since EG is the radius of the circle, AG has to be a tangent of the circle.
Already,
∠B=90∘
⇒AB⊥BE
Since BE is the radius of the circle, AB has to be a tangent of the circle.
Justification
The construction can be justified by proving that AG and AB are the tangents to the circle. For this, join EG.
∠AGE is an angle in the semi-circle. We know that an angle in a semi-circle is a right angle.
∴∠AGE=90∘
⇒EG⊥AG
Since EG is the radius of the circle, AG has to be a tangent of the circle.
Already,
∠B=90∘
⇒AB⊥BE
Since BE is the radius of the circle, AB has to be a tangent of the circle.
