A quadrilateral PQRS is drawn to circumscribe a circle.If PQ = 12 cm, QR = 15 cm and RS = 14 cm, then find the length of SP is
Question
A quadrilateral PQRS is drawn to circumscribe a circle.
If
- PQ = 12 cm,
- QR = 15 cm and
- RS = 14 cm,
then find the length of SP.
Solution
This problem can be solved using the properties of a tangential quadrilateral (a quadrilateral that circumscribes a circle).
In a tangential quadrilateral, the sum of opposite sides is equal. This means that PQ + RS = QR + SP.
We know that PQ = 12 cm, QR = 15 cm, and RS = 14 cm. We can substitute these values into the equation:
12 cm + 14 cm = 15 cm + SP
This simplifies to:
26 cm = 15 cm + SP
To solve for SP, we subtract 15 cm from both sides of the equation:
26 cm - 15 cm = SP
So, SP = 11 cm.
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