With the vertices of Δ PQR as centres, three circles are described, each touching the other two externally. If the sides of the triangle are 7 cm, 8 cm and 11 cm, find the radii of the three circles.
Circles
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Question

With the vertices of Δ PQR as centres, three circles are described, each touching the other two externally. If the sides of the triangle are 7 cm, 8 cm and 11 cm, find the radii of the three circles.

KnowledgeBoat · Accepted Answer

Let radius of circles with center P, Q and R be r1, r2 and r3. ⇒ PQ = r1 + r2 = 7 …………(1) ⇒ PR = r1 + r3 = 8 …………(2) ⇒ QR = r2 + r3 = 11 ………….(3) Adding all the above equations, we get ⇒ r1 + r2 + r1 + r3 + r2 + r3 = 7 + 8 + 11 ⇒ 2(r1 + r2 + r3) = 26 ⇒ r1 + r2 + r3 = ​ ⇒ r1 + r2 + r3 = 13 cm ………..(4) Substituting value of r2 + r3 = 11 in equation (4) we get : ⇒ r1 + 11 = 13 ⇒ r1 = 13 - 11 ⇒ r1 = 2 cm. Substituting value of r1 + r2 = 7 in equation (4) we get : ⇒ 7 + r3 = 13 ⇒ r3 = 13 - 7 ⇒ r3 = 6 cm. Substituting value of r1 + r3 = 8 in equation (4) we get : ⇒ 8 + r2 = 13 ⇒ r2 = 13 - 8 ⇒ r2 = 5 cm. Hence, the radii of the circles with center P, Q and R are 2 cm, 5 cm and 6 cm.

Mathematics

With the vertices of Δ PQR as centres, three circles are described, each touching the other two externally. If the sides of the triangle are 7 cm, 8 cm and 11 cm, find the radii of the three circles.

Circles

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