Question
Download Solution PDFTwo concentric circles of radii 15 cm and 13 cm are given. Find the length of the chord of the larger circle which touches the smaller circle.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Radius of large circle (R) = 15 cm.
Radius of small circle (r) = 13 cm
Concept used:
A line drawn from the centre of the circle to a chord bisects the chord into two halves.
The tangent to the circle is perpendicular to the radius of the circle at the point of contact.
Pythagorean theorem:
H2 = P2 + B2
Where, H = hypotenuse ; P = perpendicular ; B = base
Calculation:
Here, O is the centre and PQ is the chord of the circle.
In △POR
⇒ OP2 = OR2 + PR2
⇒ (15)2 = (13)2 + PR2
⇒ PR2 = 225 - 169 = 56
⇒ PR = √56 = 2√14 cm
PQ is tangent so, OR ⊥ PQ
PQ = PR + RQ
⇒ 2√14 + 2√14 (As PR = RQ)
⇒ 4√14 cm
∴ The correct answer is 4√14 cm.
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