Question

aha
P Q R is an Isosceles triangle
with P Q 2 PR2 10 cm and a R = 12cm.
-The hought from pon Q R 38 cm
- Find area of A P Q R What will be
the height on from a
on
PR ?​

Answer 1

Given : PQR is an isosceles triangle with PQ = PR = 25 cm, QR = 14 cm

Construction : Let X be the mid point of QR, Join PX

Then PX ⊥ QR  (Median of an isosceles triangle is perpendicular to the base)

⇒ Center of the circle O lies on PX  (perpendicular bisector of a chord passes through its center)

⇒ QX = RX = QR/2 = 14/2 cm = 7cm

In right Δ PXR

(PX)2 + (XR)2 = (PR)2

⇒ (PX)2 = (PR)2 - (XR)2 = (25 cm)2 - (7 cm)2 = (625 - 49) cm2 = 576 cm2

⇒ PX = 24 cm

Now, required radius = OP = OR = x cm(say)

⇒ OX = PX - OP = (24 - x) cm

In right Δ OXR

(OX)2 + (XR)2 = (OR)2

⇒ (24 - x)2 + 72 = x2

⇒ 242 + x2 - 2 × 24 × x + 49 = x2

⇒ 576 + x2 - 48x + 49 - x2 = 0

⇒ 48x = 625

⇒ x = 625/48 ~ 13.02

Hence required radius is 13.02  cm