Question

`square`ABCD is a rectangle. Taking AD as a diameter, a semicircle AXD is drawn which intersects the diagonal BD at X. If AB = 12 cm, AD = 9 cm, then find the values of BD and BX.

Answer 1

Given: AB = 12 cm, AD = 9 cm

To find: BD = ?, BX = ?

By Pythagoras theorem,

(BD)² = (AB)² + (AD)²

∴ (BD)² = (12)² + (9)² 

∴ (BD)² = 144 + 81

∴ (BD)² = 225

Taking square root on both sides, we get

∴ BD = `sqrt225`

∴ BD = 15 cm

By Tangent secant segment theorem,

AB² = BX × BD

∴ 12² = BX × 15

∴ BX = `144/15`

∴ BX = 9.6 cm