PQR is an isosceles triangle inscribed in a circle. If PQ = PR = 25 cm and QR = 14 cm, calculate the radius of the circle to the nearest cm.
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Question

PQR is an isosceles triangle inscribed in a circle. If PQ = PR = 25 cm and QR = 14 cm, calculate the radius of the circle to the nearest cm.

KnowledgeBoat · Accepted Answer

Given, PQ = PR = 25 cm In an isosceles triangle, the perpendicular from a vertex between equal sides bisects the opposite side. Thus, S is the mid-point of QR. QS = = 7 cm. PS is perpendicular bisector of QR and perpendicular from center bisects the chord. Thus, centre of the circle O lies on PS. Let radius of circle OQ be r. In right-angled triangle PSQ, By pythagoras theorem, ⇒ Hypotenuse2 = Perpendicular2 + Base2 ⇒ PQ2 = PS2 + SQ2 ⇒ 252 = PS2 + 72 ⇒ 625 = PS2 + 49 ⇒ PS2 = 625 - 49 ⇒ PS2 = 576 ⇒ PS = = 24 cm OS = PS - OP = 24 - r In right-angled triangle OSQ, By pythagoras theorem, ⇒ Hypotenuse2 = Perpendicular2 + Base2 ⇒ OQ2 = OS2 + SQ2 ⇒ r2 = (24 - r)2 + 72 ⇒ r2 = r2 - 48r + 576 + 49 ⇒ 48r = 625 ⇒ r = = 13.02 cm 13 cm Hence, radius of the circle = 13 cm.

Mathematics

PQR is an isosceles triangle inscribed in a circle. If PQ = PR = 25 cm and QR = 14 cm, calculate the radius of the circle to the nearest cm.

Circles

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