Given that <span>∆abc is isosceles and ab = bc, then m<bac = m<acb and m<hbc = 180 - m<bac - m<acb
Given that </span><span>m∠hbc = m∠bac +m∠bch, then m<hbc + m<bch = m<bac + 2m<bch
But m<hbc + m<bch = 90°, thus 90° = m<bac + 2m<bch
</span><span>Also, m∠bac + m∠ach = 90° ⇒ m<bac + 2m<bch = m<bac + m<ach ⇒ 2m<bch = m<ach
Since, Δabc is isosceles with ab = bc ⇒ m<bac = m<acb.
Also, m<acb = m<ach + m<bch ⇒ m<acb = 3m<bch = m<bac
</span><span><span>Since m<bch : m<ach = 1 : 2 ⇒ bh : ah = 1 : 2
Thus,
Given that ch = 84 cm, then
Now,
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Given that </span><span>m∠hbc = m∠bac +m∠bch, then m<hbc + m<bch = m<bac + 2m<bch
But m<hbc + m<bch = 90°, thus 90° = m<bac + 2m<bch
</span><span>Also, m∠bac + m∠ach = 90° ⇒ m<bac + 2m<bch = m<bac + m<ach ⇒ 2m<bch = m<ach
Since, Δabc is isosceles with ab = bc ⇒ m<bac = m<acb.
Also, m<acb = m<ach + m<bch ⇒ m<acb = 3m<bch = m<bac
</span><span><span>Since m<bch : m<ach = 1 : 2 ⇒ bh : ah = 1 : 2
Thus,
Given that ch = 84 cm, then
Now,
</span> </span>