Using ruler and a pair of compasses only, construct a triangle PQR such that PQ = 6cm and angle PQR = 70 degrees. Construct perpendicular by setter of |PQ| and |QR|. Name the intersection of the mediatos D. Draw a circle with O as center and |OD| as radius.

Question

Asked on July 13, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-07-13T17:05:53.455Z

Here are the steps to perform the geometric construction: Note on Angle Construction: An angle of 70^ cannot be constructed using only a ruler and compasses. For this specific step, a protractor is typically used in practical geometry. The following steps assume a protractor is used to set the 70^ angle, while all other constructions adhere to the "ruler and compasses only" rule. Step 1: Construct PQR Draw a straight line segment PQ with a length of 6 cm. Place the center of a protractor at point Q and mark an angle of 70^ from PQ. Draw a ray QX from Q through this mark. With Q as the center and a radius of 4 cm, draw an arc that intersects the ray QX. Label the intersection point R. Draw a straight line segment connecting points P and R to complete PQR. Step 2: Construct perpendicular bisectors and locate point O To construct the perpendicular bisector of PQ: Place the compass needle at point P and open it to a radius greater than half the length of PQ. Draw an arc above and an arc below PQ. Without changing the compass radius, place the needle at point Q and draw two more arcs that intersect the first two arcs. Draw a straight line through the two points where the arcs intersect. This is the perpendicular bisector of PQ. To construct the perpendicular bisector of QR: Place the compass needle at point Q and open it to a radius greater than half the length of QR. Draw an arc above and an arc below QR. Without changing the compass radius, place the needle at point R and draw two more arcs that intersect the previous two arcs. Draw a straight line through the two points where the arcs intersect. This is the perpendicular bisector of QR. Label the point where the two perpendicular bisectors intersect as O. Step 3: Draw the circumcircle Place the compass needle at point O (the center) and open it to the length of OP (the radius). Draw a circle. This circle should pass through points P, Q, and R. The final answer is the completed geometric construction as described above. Send me the next one 📸

Accepted Answer · 2026-07-13T17:05:53.455Z

Here are the steps to perform the geometric construction: Note on Angle Construction: An angle of 70^ cannot be constructed using only a ruler and compasses. For this specific step, a protractor is typically used in practical geometry. The following steps assume a protractor is used to set the 70^ angle, while all other constructions adhere to the "ruler and compasses only" rule. Step 1: Construct PQR Draw a straight line segment PQ with a length of 6 cm. Place the center of a protractor at point Q and mark an angle of 70^ from PQ. Draw a ray QX from Q through this mark. With Q as the center and a radius of 4 cm, draw an arc that intersects the ray QX. Label the intersection point R. Draw a straight line segment connecting points P and R to complete PQR. Step 2: Construct perpendicular bisectors and locate point O To construct the perpendicular bisector of PQ: Place the compass needle at point P and open it to a radius greater than half the length of PQ. Draw an arc above and an arc below PQ. Without changing the compass radius, place the needle at point Q and draw two more arcs that intersect the first two arcs. Draw a straight line through the two points where the arcs intersect. This is the perpendicular bisector of PQ. To construct the perpendicular bisector of QR: Place the compass needle at point Q and open it to a radius greater than half the length of QR. Draw an arc above and an arc below QR. Without changing the compass radius, place the needle at point R and draw two more arcs that intersect the previous two arcs. Draw a straight line through the two points where the arcs intersect. This is the perpendicular bisector of QR. Label the point where the two perpendicular bisectors intersect as O. Step 3: Draw the circumcircle Place the compass needle at point O (the center) and open it to the length of OP (the radius). Draw a circle. This circle should pass through points P, Q, and R. The final answer is the completed geometric construction as described above. Send me the next one 📸

Using ruler and a pair of compasses only, construct a triangle PQR such that PQ = 6cm and angle PQR = 70 degrees. Construct perpendicular by setter of |PQ| and |QR|. Name the intersection of the mediatos D. Draw a circle with O as center and |OD| as radius.

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Using ruler and a pair of compasses only, construct a triangle PQR such that PQ = 6cm and angle PQR = 70 degrees. Construct perpendicular by setter of |PQ| and |QR|. Name the intersection of the mediatos D. Draw a circle with O as center and |OD| as radius.

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